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	8680m	Isogeny class
Conductor	8680	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-1013023773440 = -1 · 28 · 5 · 77 · 312	Discriminant
Eigenvalues	2-  3 5+ 7+ -3  1  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22468,1297172]	[a1,a2,a3,a4,a6]
j	-4899784645684224/3957124115	j-invariant
L	3.4827199272415	L(r)(E,1)/r!
Ω	0.87067998181037	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	17360l1 69440bm1 78120o1 43400i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680m1

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
-	3	+	+	-3	1	3	-6	4	1	+	2	0	2	5	6	6	10	16	-4	-6	7	12	-12	9

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Quadratic twists for elliptic curve 8680m1

-4	8	-3	5	-7
17360l1	69440bm1	78120o1	43400i1	60760bb1

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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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