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
Δ	-476358400 = -1 · 28 · 52 · 74 · 31	Discriminant
Eigenvalues	2+  2 5+ 7+  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,84,980]	[a1,a2,a3,a4,a6]
Generators	[38:240:1]	Generators of the group modulo torsion
j	253012016/1860775	j-invariant
L	5.6048062255133	L(r)(E,1)/r!
Ω	1.2098574417153	Real period
R	2.3163085303534	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	17360k2 69440bk2 78120be2 43400r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680d2

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 8680d2

-4	8	-3	5	-7
17360k2	69440bk2	78120be2	43400r2	60760o2

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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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