Cremona's table of elliptic curves

12614 = 2 · 7 · 17 · 53

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+ 53-	Signs for the Atkin-Lehner involutions
Class	12614g	Isogeny class
Conductor	12614	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	324055072768 = 220 · 73 · 17 · 53	Discriminant
Eigenvalues	2-  1  2 7+  3 -2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2372,34832]	[a1,a2,a3,a4,a6]
Generators	[8:124:1]	Generators of the group modulo torsion
j	1475975706633793/324055072768	j-invariant
L	8.8522522016639	L(r)(E,1)/r!
Ω	0.91022426344479	Real period
R	0.48626764618216	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	100912x1 113526i1 88298z1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12614g1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	1	2	+	3	-2	+	-8	-2	8	-3	-8	0	-6	1	-	1	-10	-13	-6	0	10	-4	8	19

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Quadratic twists for elliptic curve 12614g1

-4	-3	-7
100912x1	113526i1	88298z1

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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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