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	8680c	Isogeny class
Conductor	8680	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	421917440000 = 211 · 54 · 73 · 312	Discriminant
Eigenvalues	2+  2 5+ 7+  0 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14376,-657940]	[a1,a2,a3,a4,a6]
Generators	[63691551:-871292150:250047]	Generators of the group modulo torsion
j	160449423671378/206014375	j-invariant
L	5.4313883819863	L(r)(E,1)/r!
Ω	0.43603465370462	Real period
R	12.456322762057	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17360j2 69440bi2 78120bd2 43400q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680c2

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

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Quadratic twists for elliptic curve 8680c2

-4	8	-3	5	-7
17360j2	69440bi2	78120bd2	43400q2	60760n2

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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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