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	8680f	Isogeny class
Conductor	8680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-1143736518400 = -1 · 28 · 52 · 78 · 31	Discriminant
Eigenvalues	2+  2 5+ 7- -4  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3836,-103660]	[a1,a2,a3,a4,a6]
j	-24391176723664/4467720775	j-invariant
L	2.402595892455	L(r)(E,1)/r!
Ω	0.30032448655688	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	17360a2 69440bv2 78120bk2 43400n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680f2

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	0	0	-4	-6	10	+	4	10	2	-12	12	12	10	-4	16	4	8	-14	6	14

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Quadratic twists for elliptic curve 8680f2

-4	8	-3	5	-7
17360a2	69440bv2	78120bk2	43400n2	60760p2

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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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