Cremona's table of elliptic curves

8680 = 2³ · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	8680l	Isogeny class
Conductor	8680	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	34442240 = 210 · 5 · 7 · 312	Discriminant
Eigenvalues	2- -2 5+ 7+ -2 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-736,7440]	[a1,a2,a3,a4,a6]
Generators	[-16:124:1] [19:26:1]	Generators of the group modulo torsion
j	43116861316/33635	j-invariant
L	4.0153711073653	L(r)(E,1)/r!
Ω	2.0514358180481	Real period
R	1.9573466895912	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17360g2 69440be2 78120l2 43400h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680l2

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

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Quadratic twists for elliptic curve 8680l2

-4	8	-3	5	-7
17360g2	69440be2	78120l2	43400h2	60760z2

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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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