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	12376n	Isogeny class
Conductor	12376	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	7063626752 = 210 · 74 · 132 · 17	Discriminant
Eigenvalues	2-  0 -2 7-  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13571,608494]	[a1,a2,a3,a4,a6]
Generators	[54:182:1]	Generators of the group modulo torsion
j	269935066988388/6898073	j-invariant
L	3.9017526052899	L(r)(E,1)/r!
Ω	1.2307482008617	Real period
R	0.79255704021302	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	24752a1 99008be1 111384ba1 86632y1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376n1

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
-	0	-2	-	2	+	+	0	2	8	-4	-2	0	4	8	2	-12	-8	0	-12	12	-2	0	14	12

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Quadratic twists for elliptic curve 12376n1

-4	8	-3	-7
24752a1	99008be1	111384ba1	86632y1

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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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