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	8680j	Isogeny class
Conductor	8680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-45778042240000 = -1 · 210 · 54 · 74 · 313	Discriminant
Eigenvalues	2- -2 5+ 7+  2  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,6664,-247040]	[a1,a2,a3,a4,a6]
j	31956819437084/44705119375	j-invariant
L	0.67881577277635	L(r)(E,1)/r!
Ω	0.33940788638818	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	17360h1 69440bf1 78120m1 43400f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680j1

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	0	-2	4	-8	0	+	4	-2	-6	0	-4	8	0	-4	8	-6	8	2	6	-18

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Quadratic twists for elliptic curve 8680j1

-4	8	-3	5	-7
17360h1	69440bf1	78120m1	43400f1	60760x1

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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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