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
Δ	-44356315867136 = -1 · 211 · 78 · 13 · 172	Discriminant
Eigenvalues	2-  0 -2 7-  2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13051,657270]	[a1,a2,a3,a4,a6]
Generators	[62:294:1]	Generators of the group modulo torsion
j	-120039762869154/21658357357	j-invariant
L	3.9017526052899	L(r)(E,1)/r!
Ω	0.61537410043087	Real period
R	1.585114080426	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	24752a2 99008be2 111384ba2 86632y2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376n2

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 12376n2

-4	8	-3	-7
24752a2	99008be2	111384ba2	86632y2

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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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