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	12376i	Isogeny class
Conductor	12376	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	45056	Modular degree for the optimal curve
Δ	1193752921088 = 210 · 74 · 134 · 17	Discriminant
Eigenvalues	2- -2  4 7+ -6 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-14056,-643968]	[a1,a2,a3,a4,a6]
j	299943806051236/1165774337	j-invariant
L	0.87712818270157	L(r)(E,1)/r!
Ω	0.43856409135078	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24752k1 99008o1 111384p1 86632bc1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376i1

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	4	+	-6	+	+	-4	-8	0	8	0	-6	0	0	2	-8	-4	-8	4	-10	8	-8	2	10

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Quadratic twists for elliptic curve 12376i1

-4	8	-3	-7
24752k1	99008o1	111384p1	86632bc1

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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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