Cremona's table of elliptic curves

34112 = 2⁶ · 13 · 41

Class	r	Atkin-Lehner	Eigenvalues
34112a (1 curve)	0	2+ 13+ 41-	2+ -1 -2  2  6 13+  0  4
Curve Equation t 34112a1 [0,-1,0,31,-287] 1
34112b (1 curve)	0	2+ 13+ 41-	2+ -1 -3  5 -6 13+  3  8
Curve Equation t 34112b1 [0,-1,0,2623,-432959] 1
34112c (1 curve)	2	2+ 13+ 41-	2+ -3  0 -2  0 13+ -2 -4
Curve Equation t Generators 34112c1 [0,0,0,-220,1264] 1 [-14:40:1]&[10:8:1]
34112d (1 curve)	2	2+ 13- 41+	2+ -1 -1 -1  2 13- -5  0
Curve Equation t Generators 34112d1 [0,-1,0,-108321,13768609] 1 [-365:2132:1]&[25:3328:1]
34112e (1 curve)	0	2+ 13- 41+	2+ -1  2  2  2 13-  4  0
Curve Equation t 34112e1 [0,-1,0,-10977,1048417] 1
34112f (1 curve)	2	2+ 13- 41+	2+ -1 -4  2 -4 13- -2  0
Curve Equation t Generators 34112f1 [0,-1,0,175,-1679] 1 [21:-104:1]&[15:64:1]
34112g (1 curve)	0	2+ 13- 41+	2+  3 -1  3  6 13-  7  4
Curve Equation t 34112g1 [0,0,0,212,-496] 1
34112h (1 curve)	2	2+ 13- 41+	2+ -3 -1 -3 -6 13-  7 -4
Curve Equation t Generators 34112h1 [0,0,0,212,496] 1 [-2:8:1]&[5:41:1]
34112i (1 curve)	0	2+ 13- 41+	2+ -3 -2 -2  2 13-  0  0
Curve Equation t 34112i1 [0,0,0,-48556,-4185296] 1
34112j (4 curves)	1	2+ 13- 41-	2+  0  2  0  0 13- -6  8
Curve Equation t Generators 34112j1 [0,0,0,-10604,399280] 2 [45:115:1] 34112j2 [0,0,0,-31084,-1607760] 4 [-14855:79833:125] 34112j3 [0,0,0,73876,-10130512] 4 [1677216255:31592253727:7414875] 34112j4 [0,0,0,-463724,-121535568] 2 [30882:784576:27]
34112k (2 curves)	1	2+ 13- 41-	2+  2 -2  4  0 13- -6  8
Curve Equation t Generators 34112k1 [0,-1,0,-709,-7035] 2 [33090716736:428684169851:191102976] 34112k2 [0,-1,0,-689,-7471] 2 [501831:13147264:729]
34112l (1 curve)	1	2+ 13- 41-	2+  3 -1  3 -6 13-  3 -4
Curve Equation t Generators 34112l1 [0,0,0,-34828,-5836816] 1 [8879010:454197248:3375]
34112m (1 curve)	1	2- 13+ 41-	2-  1 -2 -2 -6 13+  0 -4
Curve Equation t Generators 34112m1 [0,1,0,31,287] 1 [-1:16:1]
34112n (1 curve)	1	2- 13+ 41-	2-  1 -3 -5  6 13+  3 -8
Curve Equation t Generators 34112n1 [0,1,0,2623,432959] 1 [-1:656:1]
34112o (1 curve)	1	2- 13+ 41-	2-  3  0  2  0 13+ -2  4
Curve Equation t Generators 34112o1 [0,0,0,-220,-1264] 1 [188832:483652:9261]
34112p (1 curve)	1	2- 13- 41+	2-  1 -1  1 -2 13- -5  0
Curve Equation t Generators 34112p1 [0,1,0,-108321,-13768609] 1 [2497:123656:1]
34112q (1 curve)	1	2- 13- 41+	2-  1  2 -2 -2 13-  4  0
Curve Equation t Generators 34112q1 [0,1,0,-10977,-1048417] 1 [28955:372736:125]
34112r (1 curve)	1	2- 13- 41+	2-  1 -4 -2  4 13- -2  0
Curve Equation t Generators 34112r1 [0,1,0,175,1679] 1 [5:52:1]
34112s (1 curve)	1	2- 13- 41+	2-  3 -2  2 -2 13-  0  0
Curve Equation t Generators 34112s1 [0,0,0,-48556,4185296] 1 [-6738:23552:27]
34112t (4 curves)	0	2- 13- 41-	2-  0  2  0  0 13- -6 -8
Curve Equation t 34112t1 [0,0,0,-10604,-399280] 2 34112t2 [0,0,0,-31084,1607760] 4 34112t3 [0,0,0,73876,10130512] 2 34112t4 [0,0,0,-463724,121535568] 4
34112u (2 curves)	2	2- 13- 41-	2- -2 -2 -4  0 13- -6 -8
Curve Equation t Generators 34112u1 [0,1,0,-709,7035] 2 [-10:115:1]&[-1:88:1] 34112u2 [0,1,0,-689,7471] 2 [-13:120:1]&[-5:104:1]
34112v (1 curve)	0	2- 13- 41-	2- -3 -1 -3  6 13-  3  4
Curve Equation t 34112v1 [0,0,0,-34828,5836816] 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
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