Cremona's table of elliptic curves

12376 = 2³ · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 13- 17-	Signs for the Atkin-Lehner involutions
Class	12376p	Isogeny class
Conductor	12376	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-114453248 = -1 · 28 · 7 · 13 · 173	Discriminant
Eigenvalues	2- -1 -2 7- -1 13- 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-124,-700]	[a1,a2,a3,a4,a6]
Generators	[16:34:1]	Generators of the group modulo torsion
j	-830321872/447083	j-invariant
L	3.0396699403783	L(r)(E,1)/r!
Ω	0.69731108844001	Real period
R	0.36326086385854	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	24752i1 99008z1 111384be1 86632q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376p1

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	-	-1	-	-	-5	6	0	-6	-3	6	1	3	1	4	10	16	0	0	-16	-9	1	-2

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Quadratic twists for elliptic curve 12376p1

-4	8	-3	-7
24752i1	99008z1	111384be1	86632q1

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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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