Cremona's table of elliptic curves

680 = 2³ · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	680a	Isogeny class
Conductor	680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	184960000 = 210 · 54 · 172	Discriminant
Eigenvalues	2-  0 5+  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-163,462]	[a1,a2,a3,a4,a6]
Generators	[2:12:1]	Generators of the group modulo torsion
j	467720676/180625	j-invariant
L	2.0532909813083	L(r)(E,1)/r!
Ω	1.6375152617685	Real period
R	2.5078129398206	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1360a2 5440h2 6120k2 3400a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680a2

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

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Quadratic twists for elliptic curve 680a2

-4	8	-3	5	-7	-11	13	17
1360a2	5440h2	6120k2	3400a2	33320q2	82280a2	114920f2	11560j2

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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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