Cremona's table of elliptic curves

23985 = 3² · 5 · 13 · 41

Class	r	Atkin-Lehner	Eigenvalues
23985a (1 curve)	1	3+ 5+ 13+ 41+	-2 3+ 5+  2 -3 13+ -3 -6
Curve Equation t Generators 23985a1 [0,0,1,-774903,-262563496] 1 [2052:82387:1]
23985b (1 curve)	0	3+ 5+ 13+ 41-	2 3+ 5+ -2  3 13+  3  2
Curve Equation t 23985b1 [0,0,1,27,-14047] 1
23985c (1 curve)	2	3+ 5- 13+ 41+	-2 3+ 5- -2 -3 13+ -3  2
Curve Equation t Generators 23985c1 [0,0,1,3,520] 1 [8:32:1]&[-5:19:1]
23985d (1 curve)	1	3+ 5- 13+ 41-	2 3+ 5-  2  3 13+  3 -6
Curve Equation t Generators 23985d1 [0,0,1,-6974127,7089214385] 1 [7874:274621:8]
23985e (4 curves)	0	3- 5+ 13+ 41+	1 3- 5+  0  0 13+  2  4
Curve Equation t 23985e1 [1,-1,0,225,0] 2 23985e2 [1,-1,0,-900,675] 4 23985e3 [1,-1,0,-9675,-362610] 2 23985e4 [1,-1,0,-10125,393660] 2
23985f (2 curves)	1	3- 5+ 13+ 41-	1 3- 5+ -2  4 13+  6 -8
Curve Equation t Generators 23985f1 [1,-1,0,-12465,-532544] 2 [1361700:19722242:4913] 23985f2 [1,-1,0,-12060,-569075] 2 [1068:34163:1]
23985g (1 curve)	0	3- 5+ 13- 41-	2 3- 5+  2  0 13-  2  0
Curve Equation t 23985g1 [0,0,1,3327,-85847] 1
23985h (1 curve)	1	3- 5- 13+ 41+	0 3- 5-  0 -2 13+  6 -4
Curve Equation t Generators 23985h1 [0,0,1,-12,117] 1 [5:13:1]
23985i (1 curve)	1	3- 5- 13+ 41+	0 3- 5-  0  6 13+ -2  4
Curve Equation t Generators 23985i1 [0,0,1,-21295182,-37824237243] 1 [9579139889555235627980707432440317291084676290:13480912219738730626823391971239095946796633034421:4836582777103347907447877618063465477896]
23985j (2 curves)	1	3- 5- 13+ 41+	1 3- 5-  2 -2 13+ -2  6
Curve Equation t Generators 23985j1 [1,-1,0,-2182059,1241188488] 2 [6566:9717:8] 23985j2 [1,-1,0,-2153934,1274719113] 2 [8006:83877:8]
23985k (2 curves)	1	3- 5- 13+ 41+	1 3- 5- -2 -6 13+  6  2
Curve Equation t Generators 23985k1 [1,-1,0,-811989,-281423480] 2 [30612:415354:27] 23985k2 [1,-1,0,-811944,-281456267] 2 [3572:204089:1]
23985l (2 curves)	1	3- 5- 13+ 41+	1 3- 5-  4  0 13+  6  2
Curve Equation t Generators 23985l1 [1,-1,0,-549,7168] 2 [-16:116:1] 23985l2 [1,-1,0,-9774,374323] 2 [1102:9655:8]
23985m (2 curves)	1	3- 5- 13+ 41+	-1 3- 5-  2  0 13+ -2  4
Curve Equation t Generators 23985m1 [1,-1,1,-497,4384] 2 [4:47:1] 23985m2 [1,-1,1,-452,5176] 2 [4:56:1]
23985n (1 curve)	1	3- 5- 13+ 41+	-2 3- 5-  2  4 13+ -2  0
Curve Equation t Generators 23985n1 [0,0,1,-4827,-129870] 1 [1810:25745:8]
23985o (1 curve)	2	3- 5- 13+ 41-	-2 3- 5- -4  1 13+ -5  0
Curve Equation t Generators 23985o1 [0,0,1,-30027,2006010] 1 [-177:1332:1]&[233:-2768:1]
23985p (2 curves)	0	3- 5- 13- 41+	1 3- 5-  2  2 13-  2 -6
Curve Equation t 23985p1 [1,-1,0,-1224,-15957] 2 23985p2 [1,-1,0,-99,-44982] 2
23985q (2 curves)	0	3- 5- 13- 41+	1 3- 5- -4 -4 13-  2  6
Curve Equation t 23985q1 [1,-1,0,25366086,28482874695] 2 23985q2 [1,-1,0,-118774539,245299202820] 2
23985r (1 curve)	0	3- 5- 13- 41+	1 3- 5- -4  6 13- -8  6
Curve Equation t 23985r1 [1,-1,0,-1224,-16295] 1
23985s (4 curves)	1	3- 5- 13- 41-	-1 3- 5-  0  4 13- -2  4
Curve Equation t Generators 23985s1 [1,-1,1,-392,6306] 4 [24:89:1] 23985s2 [1,-1,1,-7997,277044] 4 [14:402:1] 23985s3 [1,-1,1,-9752,147876] 2 [-54:744:1] 23985s4 [1,-1,1,-127922,17642184] 2 [219:198:1]

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

Part of Computational Number Theory
Back to Tables and computations