Here are the data collected regarding curves of the form
	y^2=x(x^2-x+(1-T^10)/5)
for some values of  T  (more or less randomly selected). For each  T  we
give the rank and generators. Rank is usually the number of generators
found; in about 20 cases the listed rank is one greater (i.e. another generator
is expected but not yet found) by parity considerations; the number of
generators so far found is in parentheses. (In a few cases these number differ
by 2, accounting for parity on both  E/phi(E') and E'/phi(E).) Finally, in
5 cases the best upper bound on the rank exceeds the number of generators by
2, so the rank is not yet really known. Rank is then shown in the form  "2..4"
	Generators are listed by the  x-coordinates. The choice of generators
is not consistent from curve to curve, sorry. A few marked [%] were only
obtained after the parameterization was available.
	Some comments follow the table; others available at
http://www.math.niu.edu/~rusin/research-math/funny.crv/

T	Rank	Generators
==============================================================================
0:	0	[note: we now know this is the _only_  T  giving rank=0]
1: curve is singular
2:	2	3*5		2^6*11*31/5^2
3:	2	23^2*61/15^2	11^2*31^2*43^2/(180*7)^2
4:	2	3*5*7^2*41	2^2*5*11*31*41/17^2
5:	4	2^2*5*71	11*71*521/10^2	2^2*5*71*521/23^2 19^2*521/5^2
6:	1	(5*11*101*311)*(11*53*151/2/3/19/131^2)^2
7:	2	11^3*127^2*191/75^2	-3*5*(2^2*7*5642251/47/150503)^2
8:	2	5*7^3*11*151/3^2	2^2*11^3*31*151*331/(5*137)^2
9:	1	5*61*1181*(11*29*67493/3^2/8500399)^2
10:	3	3^2*11*41*9091/20^2	11*271*(3*7*19*16267/2/5/57373)^2	(2*3*313*1663*13013963/5/17/29/139/331/479)^2
11:	4	2^2*3^3*5*13421*3221/41^2	2*3*41^2*13421/25^2	5^3*13421*3221/122^2	5*43^4*3221/24^2
12:	2	-1*( 3*19^2*1805143/5/5336297  )^2	-5*11*13*( 2^2*3*41*191*54521/523/885187 )^2
13:	3	2*3*5*7*2411	2^2*3*7^3*11*2411/5^2	-2411*(2*206179*208111/5/23/258593789)^2
14:	2	17^2*101*3761/18^2	-3*13*(2*7*39409*7451/5^2/41/127/479)^2
15:	1	-2*5*7*(2^2*5*3*19*79*1699799/2688492601)^2
16:	3	11*31*83^2/2^2	2^4*11*31*2011^2/65^2	2^2*5^3*11^3*31*41*61681/5347^2
17:	2(1)	-10*(2^2*3*17*131*1451*36571/11/53/12421567)^2
==============================================================================
1/2:	2	11/10^2		3*5^3*11/56^2
3/2:	2	3^2*5^3/8^2	5^3*11*17^2*211/(24*169)^2
5/2:	3	3*7*41*1031/130^2	5*11^3/12^2	3^3*7*11*19^2/100^2
7/2:	2	3^2*61*73^2/104^2	-1*(3*7*19*54851/2^2/447637)^2
9/2:	2(1)	-5*7*11*(3^2*191*213091/2^2/67091341)^2	
17/2:	2	3*5^3*11*19*74731/(8*29)^2	 3*19*1721*(277*661*65551/2^5/13/59818943)^2
19/2:	2(1)	(-3*5*7*17)*(19*16791162781/2^2/23/53/137/114167)^2
==============================================================================
1/3:	2	61/15^2 	11^2*31^2*61/(135*19)^2
2/3:	2	5*11/27^2 	5^3*7^2*11*13^2/(9*19*23)^2
5/3:	1	11*131*421*(523*4507/27/25/41/2579)^2
7/3:	2	2^2*5*11*13^2*31/7^2	-2*(2*7*19*44621/3^2/11/137/499)^2
8/3:	2	2^2*29^2*37^2/135^2	2^2*5^3*23^2*1301*3001/(27*443)^2
10/3:	2	2^2*5*139^2*701/(9*23)^2	(-5*7*13)*(2*5*599*148961/3^2/59/3462779)^2
11/3:	2	41*103^2*281*20101/(270*53)^2	( 17*137*2618849327/3^3/5/42923/42899 )^2
13/3:	3	2^4*41*2111/45^2	2^7*11*181*269^2/(3^7)^2	5*11*41*73^2*181*2111/(162*461)^2
19/3:	2(1)	-2*5*11*(2^2*19*7219*2290969/3^2/189617/114473)^2
26/3:	2..4(2)	7^2*29*311*409711/270^2	(11*29*151)*(131*2969*2593/2^2/3^3/5/43/64037)^2
29/3:	3	2^5*13*71*4423^2/(135*23)^2	(2*11*13*41*271*58271)*(2^2*23*79*7589/3^3/5/137/4600027 )^2 	(2*1341*271)*(2^2*256219*99401/3^3/5/2035161343)^2
==============================================================================
1/4:	3	5*31/32^2	11*41/96^2	3*11*41/128^2
3/4:	3	3^4*11*181/800^2	5*7^3*71*181/(192*67)^2	3^2*31^2*43^2*71/(160*557)^2
7/4:	1	1621*5261*( 29*1083749/2^6/5/7/41/71/751 )^2
9/4:	2	95923^2/(64*15*11)^2	5*7^2*11^3*211*4621/(2^7*3*257)^2
11/4:	3	5^3*22861*2161/(2^7*11)^2     7*17^2*47^2/96^2	7*2161*( 1613/2^5/3^6 )^2
13/4:	1	181*41141*( 11^2*155757971/2^6/5/13/409/1091/1619 )^2
==============================================================================
1/5:	3	11*71/5^5	 7^2/5^5	 2^17*3^3/5^8
3/5:	2	2^4*3^2*5*149^2/(125*389)^2	2^4*11*13^2*131^3/(1125*487)^2
9/5:	1	(11*31*41*4441)*( 221781121/3^2/5^4/71/262501 )^2
11/5:	1	31*331*26321*(768176281/5^4/11/19/7768249)^2
12/5:	2	2^2*3^6*5*14821/125^2	(11*3191)*(2*3*1487*441107/7/71/1171/1987/5^3)^2
13/5:	2	3^2*37^2*61*46021/(125*7*29)^2	(11*31)*(3*29*47*349*54311/2/5^3/113/5204867)^2
14/5:	5	19*71*491/5^5	7^2*11^2*19*491/500^2 	3^4*11^2*71*401*491/(250*127)^2 	5*19*71*491*601^2/(5^3*7*139)^2 	3^2*7^2*11^2*19*257^2*491/(4000*139)^2
16/5:	1	61*101*821*941*( 29*115981*2729/2^4/5^4/211/17939461 )^2
17/5:	4	71*911*118061/(125*31)^2	 2*3^3*5*11*71*118061/(125*41)^2	 2*3*967^2/125^2	 5*11*151^2*911/2000^2
19/5:	4	-2*7*( 47*61/5^3/13 )^2	-2*3*11*( 2*3^2/5^4 )	2*7*11*9391*(2*41/3/5^3/13)^2 	3*7*11*5*9391*( 563/2/5^3/181 )^2
21/5:	2	-11*31*41*461*6221*( 2^2*3*156841/5^4/52756807 )^2	-(2^2*3*59*930606811*3061/5^4/1901981/71941)^2
27/5:	1	-5*11*(2^3*3^3*19*14318765849/5^2/971/402710411)^2
29/5:	4	3*5*17^3*54851*4721/(125*313)^2  	23^2*248851^2/(5500*19)^2	5*181*4721*(8*12973/3/125/23/61)^2	3*5*11*17*181*(41*21143/8/25/137/191)^2
37/5:	3	2^5*3*5*1051*196991/(25*7*11)^2	-11*1051*(2^3*406649/3/125/9497)^2	-3*5*7*(2^3*19*37*509*41389*8609/5^2/31/47/7793/372121)^2
43/5:	3	2*3*29531*( 1511/5^4/7 )^2	2*3*7^2*11*19*41*617^2*6791/(625*503)^2	 19*131*( 3156469/31/5^6 )^2
51/5:	2(1)	-5*7*23*(1/5^2*2^2*3*17*109*415775222039/50632537453801)^2
53/5:	5(3)	11*23^2*31*232591*792031/(125*307)^2	17^2*757^2*118787^2/(12*125*61^2)^2	5*31*41^2*1229^2*232591/125^2
==============================================================================
11/6:	3	-5*9931*( 31*317/2^4/79/45413 )^2	-6131*9931*( 19*503/2^2/3^3/5/47279 )^2	-17*(11*79*191*1321/2^2/3^2/23/373/4967)^2
13/6:	1	11*71*281*4721*( 2998226221/2^3/3^3/5/13/79/6968179 )^2
17/6:	3	5*23*(5^2*7*43/2/3^5/17)^2	-11*( 17*83*587/2^3/3^2/5/971 )^2	151052743^2/(16*27*25*11*41)^2
19/6:	5	5*31*41/6^2	 31*79^2/36^2	 5*11*41*421*641/(18*7)^2	 5^4*13*31*41*421*641/(4*27*43)^2	 5*11*13*31*37^2*41*641/(8*9*7*109)^2
==============================================================================
1/7:	2(1)	11*191*2801*( 593*10937/5/7^3/6004949 )^2
9/7:	1	11*431*21121* ( 11*23*293*6569/3^2/5/7^3/19/2069671 )^2
13/7:	1	5*11*41*131*3881*( 11*53*271279/7^3/13/7699/10301 )^2
15/7:	1	92821*35281*( 9596332201/3/5^2/7^3/19/89628521 )^2
17/7:	2	2*3*5*11*31*1931/343^2	2*3*2551*(47*617*69763/5/7^3/284483)^2
18/7:	3	3^2*5*61*151/49^2	11*101*151*2791/2499^2	-5*11*(3*138427/2^3/7^2/17/73)^2
19/7:	2(1)	-2*3*5*13*(2*19*191*73098461/7^2/1453/30612037)^2
20/7:	4(2)	11*244861*( 3900199/5/49/173/14593 )^2	(-3*5*13)*(3*5*2^2*1178231*18329/7^2/11/319469/17839)^2 [%]
23/7:	1	5*11*71*5651*3911* ( 5*1063*1223051/7^3/19/23/86161/8501 )^2
25/7:	2	5*17471*27791/(2*7*11*19)^2	5*11*31*(37*59*13219/3/7^2/191/1709)^2
==============================================================================
 3/8:	1	5*1301*3001*( 269*4973/2^9/3/461/9631 )^2
13/8:	2	-3*11*1231*( 13*59*659/2^9/103529 )^2	(5*11*71*271*1231)*(5^2*8317297/2^9/13/19/1762751)^2
19/8:	2(1)	-3*5811*(3*19*1006339*12619/2^6/367/673/218191)^2
21/8:	1..3(1)	-5*13*29*(3*7*30492651041/2^6/24931999/4159)^2
23/8:	1..3(1)	-3*31*(23*131*101145199/2^6/53/191/443/1697)^2
==============================================================================
1/9:	2	11^2*397^2/(3^6*7)^2	2^6*11^2*31^2/(27*199)^2
7/9:	1	11*431*21121*( 404398201/3^6/5/7/130398629 )^2
17/9:	3(2)	5*11*13*5171*( 17/2^4/3^5 )^2 	-170101*( 2^6/3^5/5/17 )^2
23/9:	4(2)	10*( 2^2*41*43*1109/3^6/4159 )^2	-5*7*(2^3*23*79*1109*708161/3^4/11/29/698924839)^2
1/11:	2	3^3*5*11*3221*13421/(7*1331*53)^2 2^3*3/(5*11)^2
3/11:	1..3(1)	5*7*(2^2*3*248700469/11^2/811/392251)^2
5/11:	2	2*3*11*31*331*26321*( 3*21419/5/7/37/97/127/11^3 )^2	(31*331*26321)*(233*1187*2011/5^2/11^3/322738181)^2
7/11:	2	2*5*11*41*36061*( 347*607/29^2/241/11^3 )^2	10*(3*2*7*79*211*28001/11^2/31/6037/5923)^2
13/11:	2	2*5*31*41*3391/1331^2	(2*5*541)*(14435766031/3/11^3/31/116447)^2
19/11:	3(2)	2^3*3*11*271^2*289381/(1331*337)^2	5*13^2*17581*289381/(2*1331*241)^2
21/11:	3(2)	3^2*11*31*37^2*132661/(32*5*1331)^2	(-1)*(2^3*3*7*76379*52301/5/11^2/41597/33457)^2 [%]
29/13:	3	-2*5*2791*( 1949/13^3/83 )^2	2*3*11*41*421*1181*( 3^3*1013/5/13^2/13697 )^2	-3*5*( 3*2011*9923/2^2/13^2/53/1669 )^2
37/13:	1	-3*5*(2^2*37*79*191*16979*2309/13^2/197/1755085373)^2
7/15:	3	383^2*911^2/881000^2	( 379*6546823/2^4/3/5^3/17/37/71/103 )^2	11*5*(2^2*6902557/5^3/3^3/69911)^2
31/15:	1	-2*5*23*(2^2/5^2*31*1021*5119*102409/3^2/11/308929398731)^2
1/17:	3	2^5*5*101/289^2	101*(3*89*3506969/2/5/13^2/17^3/929)^2	(2^2*65735294797*1777/5/17^3/827851/53927)^2
5/17:	1..3(1)	2*3*5*11*(2*5*8291162141/17^2/10959659041)^2
9/17:	3(1)	5*13*(2^2*3^2*1259509*9601/17^2/439/683/79133)^2
5/27:	2(1)	5*11*(2^3*5*71*739*1471*3919/3^6/10331/33168251)^2
==============================================================================


Here is what was known in January using only standard descent: for most
curves the true rank was unknown as were many generators (in particular
there were no points known on curves known to be of rank 1).

n	Total	rank=n	..or +1	..or +2	..+3	..+4	..+5	..+6	..+7
0	29(29)	1	0	7	6	7	5	2	1
1	30(16)	5(0)	2(2)	9(3)	4(4)	7(5)	1(1)	2(2)
2	24(18)	11(9)	2(2)	9(5)	1(1)	1(1)	
3	8(7)	5(4)	0	2(2)	0	1(1)
4	3(3)	2(2)	0	1(1)
5	2(2)	2(2)

In most cases lower bound on rank is due to having the right no. of gens.
The number of such cases is in parentheses. When we have fewer generators,
the number we have is  n-1. Thus:
	in 42 cases we have no generators (0)
etc., for a grand total of 104 generators up until then.


Compare to the results after using repeated descent (knowing, in addition,
the parameterization over  Q(T), and invoking parity conjectures):

n	rk=n	rk=n or n+2
0	1	0
1	19	4
2	39	1(*)  (* 26/3 is the last remaining)
3	22(*)	0     (* includes 9/17)
4	7(*)	0     (* includes 20/7, 23/9)
5	3(*)	0     (* includes 53/5)
TOT	91	5 = 96
SUM	206	6+10*ep = 212+10ep
AVG	2.26	1.20+2ep = 2.21+0.10ep = [2.21 .. 2.31]
Thus all ranks known to within  2. (All ambiguity on E/phi, not E'/phi').

(Note: ave. rank of the 2-isog. curve is only 0.26, so on average  E/phi
carries between  1.95  and  2.05  generators)

The 212 generators so far "known" to exist include 20 not yet found. Still,
this is (exactly!) 2.00 known generators per curve, average.


Note on computation time for obtaining upper bounds:
Each done in 15 mins or less each (both E and E') except for one@20min (T=14/5)
one@30min (T=43/4), and one@75mins (T=53/5) (these and 23/8 and 29/13
were the only ones with 128 hsp to examine.)

(Observe that the upper bounds so obtained certainly agree with the 
correct rank in all cases except perhaps the  5  remaining ones with
undetermined rank.)