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	12614i	Isogeny class
Conductor	12614	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	39168	Modular degree for the optimal curve
Δ	23011707686912 = 212 · 76 · 17 · 532	Discriminant
Eigenvalues	2- -2  0 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-42798,3396484]	[a1,a2,a3,a4,a6]
Generators	[126:28:1]	Generators of the group modulo torsion
j	8669514345388422625/23011707686912	j-invariant
L	5.0785372672464	L(r)(E,1)/r!
Ω	0.67827867023755	Real period
R	1.8718476232887	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	100912k1 113526r1 88298u1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12614i1

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
-	-2	0	-	0	2	+	-4	6	-6	2	2	0	-4	0	+	-12	8	8	-6	-4	2	-12	6	-10

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Quadratic twists for elliptic curve 12614i1

-4	-3	-7
100912k1	113526r1	88298u1

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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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