Cremona's table of elliptic curves

23205 = 3 · 5 · 7 · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
23205a (4 curves)	1	3+ 5+ 7+ 13+ 17+	1 3+ 5+ 7+ -4 13+ 17+ -8
Curve Equation t Generators 23205a1 [1,1,0,-285313,58539712] 2 [112:5236:1] 23205a2 [1,1,0,-285558,58433823] 4 [894:41835:8] 23205a3 [1,1,0,-157983,111071268] 2 [2014:73755:8] 23205a4 [1,1,0,-417053,-975618] 2 [42804:263523:64]
23205b (1 curve)	0	3+ 5+ 7- 13+ 17+	2 3+ 5+ 7- -6 13+ 17+ -6
Curve Equation t 23205b1 [0,-1,1,-12696,596657] 1
23205c (4 curves)	1	3+ 5+ 7- 13- 17+	-1 3+ 5+ 7-  0 13- 17+  8
Curve Equation t Generators 23205c1 [1,1,1,-1456,43328] 2 [32:159:1] 23205c2 [1,1,1,-29581,1944578] 4 [74:372:1] 23205c3 [1,1,1,-35956,1036778] 2 [-44:1614:1] 23205c4 [1,1,1,-473206,125094878] 2 [399:-122:1]
23205d (1 curve)	0	3+ 5+ 7- 13- 17-	2 3+ 5+ 7- -2 13- 17- -2
Curve Equation t 23205d1 [0,-1,1,34,-169] 1
23205e (2 curves)	1	3+ 5- 7+ 13+ 17-	1 3+ 5- 7+  2 13+ 17- -8
Curve Equation t Generators 23205e1 [1,1,0,-7,-56] 2 [950:9929:8] 23205e2 [1,1,0,-262,-1739] 2 [20:29:1]
23205f (4 curves)	1	3+ 5- 7+ 13+ 17-	1 3+ 5- 7+ -4 13+ 17-  4
Curve Equation t Generators 23205f1 [1,1,0,-55814012,160472273379] 2 [3203919722:-20361967101:704969] 23205f2 [1,1,0,-55956817,159609645496] 4 [1272:300184:1] 23205f3 [1,1,0,-13351072,396812870209] 4 [283092:41548279:64] 23205f4 [1,1,0,-100847442,-132798907629] 2 [-11074:520847:8]
23205g (4 curves)	0	3+ 5- 7+ 13- 17-	1 3+ 5- 7+  0 13- 17-  8
Curve Equation t 23205g1 [1,1,0,2308,14019] 2 23205g2 [1,1,0,-9697,102856] 4 23205g3 [1,1,0,-89322,-10232469] 2 23205g4 [1,1,0,-122152,16363849] 4
23205h (4 curves)	1	3+ 5- 7- 13+ 17+	-1 3+ 5- 7- -4 13+ 17+ -4
Curve Equation t Generators 23205h1 [1,1,1,-105,-450] 2 [-6:5:1] 23205h2 [1,1,1,-230,650] 4 [-10:50:1] 23205h3 [1,1,1,745,5720] 2 [5:95:1] 23205h4 [1,1,1,-3205,68480] 2 [35:9:1]
23205i (2 curves)	1	3- 5+ 7+ 13+ 17-	1 3- 5+ 7+ -2 13+ 17- -4
Curve Equation t Generators 23205i1 [1,0,1,-4904,132617] 2 [270:473:8] 23205i2 [1,0,1,-78599,8474891] 2 [191:567:1]
23205j (1 curve)	1	3- 5+ 7+ 13+ 17-	2 3- 5+ 7+ -2 13+ 17-  6
Curve Equation t Generators 23205j1 [0,1,1,53104,-21142165] 1 [29690:1812065:8]
23205k (2 curves)	1	3- 5- 7+ 13+ 17+	-1 3- 5- 7+ -6 13+ 17+  4
Curve Equation t Generators 23205k1 [1,0,0,-1140,25767] 2 [39:-222:1] 23205k2 [1,0,0,-21795,1236150] 2 [165:-1545:1]
23205l (4 curves)	0	3- 5- 7+ 13+ 17-	-1 3- 5- 7+  4 13+ 17-  0
Curve Equation t 23205l1 [1,0,0,-26345,6912912] 4 23205l2 [1,0,0,-729470,239084787] 4 23205l3 [1,0,0,-1046345,10998162] 2 23205l4 [1,0,0,-11662595,15328983912] 2
23205m (6 curves)	1	3- 5- 7+ 13- 17-	-1 3- 5- 7+ -4 13- 17-  4
Curve Equation t Generators 23205m1 [1,0,0,-108660,48356847] 4 [-381:6063:1] 23205m2 [1,0,0,-2765865,1766505600] 8 [-1605:46320:1] 23205m3 [1,0,0,-3819270,297426987] 4 [-1911:25818:1] 23205m4 [1,0,0,-44227740,113207733225] 4 [3840:-1875:1] 23205m5 [1,0,0,15185625,2376562500] 2 [0:48750:1] 23205m6 [1,0,0,-39678645,-95798526138] 2 [-3786:14568:1]
23205n (2 curves)	1	3- 5- 7- 13+ 17-	-1 3- 5- 7-  2 13+ 17- -4
Curve Equation t Generators 23205n1 [1,0,0,225,-55080] 2 [87:747:1] 23205n2 [1,0,0,-20430,-1100223] 2 [-81:198:1]
23205o (8 curves)	0	3- 5- 7- 13- 17-	-1 3- 5- 7-  4 13- 17-  4
Curve Equation t 23205o1 [1,0,0,-57460,5271695] 4 23205o2 [1,0,0,-90265,-1440208] 8 23205o3 [1,0,0,357260,-11375263] 4 23205o4 [1,0,0,-1062670,-420935725] 8 23205o5 [1,0,0,-690025,-720318718] 4 23205o6 [1,0,0,-16993795,-26965376200] 4 23205o7 [1,0,0,-16984870,-26995112515] 2 23205o8 [1,0,0,-271900720,-1725716105785] 2

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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