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	16	Product of Tamagawa factors cp
Δ	85372508881793168 = 24 · 72 · 173 · 536	Discriminant
Eigenvalues	2- -2  0 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-203518,-32439372]	[a1,a2,a3,a4,a6]
Generators	[966:25452:1]	Generators of the group modulo torsion
j	932249853631912614625/85372508881793168	j-invariant
L	5.0785372672464	L(r)(E,1)/r!
Ω	0.22609289007918	Real period
R	5.6155428698662	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100912k3 113526r3 88298u3	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12614i3

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 12614i3

-4	-3	-7
100912k3	113526r3	88298u3

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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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