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	8680n	Isogeny class
Conductor	8680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	301369600 = 28 · 52 · 72 · 312	Discriminant
Eigenvalues	2-  0 5- 7+  0  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-367,-2574]	[a1,a2,a3,a4,a6]
j	21354132816/1177225	j-invariant
L	2.1890339338064	L(r)(E,1)/r!
Ω	1.0945169669032	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17360n2 69440h2 78120c2 43400j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680n2

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

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Quadratic twists for elliptic curve 8680n2

-4	8	-3	5	-7
17360n2	69440h2	78120c2	43400j2	60760q2

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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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