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	8680d	Isogeny class
Conductor	8680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	3767120 = 24 · 5 · 72 · 312	Discriminant
Eigenvalues	2+  2 5+ 7+  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-71,236]	[a1,a2,a3,a4,a6]
Generators	[-5:21:1]	Generators of the group modulo torsion
j	2508888064/235445	j-invariant
L	5.6048062255133	L(r)(E,1)/r!
Ω	2.4197148834306	Real period
R	1.1581542651767	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	17360k1 69440bk1 78120be1 43400r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680d1

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	4	-4	4	-2	-6	+	4	-6	-2	-12	4	-4	-2	12	8	-16	-4	-6	2	6

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Quadratic twists for elliptic curve 8680d1

-4	8	-3	5	-7
17360k1	69440bk1	78120be1	43400r1	60760o1

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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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