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	16	Product of Tamagawa factors cp
Δ	-47635840000 = -1 · 210 · 54 · 74 · 31	Discriminant
Eigenvalues	2-  0 5- 7+  0  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,253,-10386]	[a1,a2,a3,a4,a6]
j	1748981916/46519375	j-invariant
L	2.1890339338064	L(r)(E,1)/r!
Ω	0.54725848345159	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	17360n4 69440h3 78120c3 43400j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680n4

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 8680n4

-4	8	-3	5	-7
17360n4	69440h3	78120c3	43400j3	60760q3

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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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