Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	8736s	Isogeny class
Conductor	8736	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	587651029056 = 26 · 38 · 72 · 134	Discriminant
Eigenvalues	2- 3+  2 7-  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9142,337480]	[a1,a2,a3,a4,a6]
Generators	[402:7840:1]	Generators of the group modulo torsion
j	1320428512222912/9182047329	j-invariant
L	4.3084566346815	L(r)(E,1)/r!
Ω	0.92283798511636	Real period
R	4.6687031788556	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8736v1 17472dd2 26208q1 61152cc1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736s1

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	-	0	+	-6	4	0	-2	0	-2	10	-8	0	-2	-12	-6	8	8	-14	-8	4	-14	2

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Quadratic twists for elliptic curve 8736s1

-4	8	-3	-7	13
8736v1	17472dd2	26208q1	61152cc1	113568c1

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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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