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	12376g	Isogeny class
Conductor	12376	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4064	Modular degree for the optimal curve
Δ	-24752 = -1 · 24 · 7 · 13 · 17	Discriminant
Eigenvalues	2+ -1  2 7- -1 13- 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2787,-55712]	[a1,a2,a3,a4,a6]
Generators	[2937:25847:27]	Generators of the group modulo torsion
j	-149682302445568/1547	j-invariant
L	4.4578554545279	L(r)(E,1)/r!
Ω	0.32852795598354	Real period
R	6.7845907377684	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	24752f1 99008t1 111384cq1 86632d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376g1

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	-2	-4	2	11	-10	-9	-11	1	-4	14	-8	8	4	-4	-7	-7	-14

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Quadratic twists for elliptic curve 12376g1

-4	8	-3	-7
24752f1	99008t1	111384cq1	86632d1

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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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