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
deg	64	Modular degree for the optimal curve
Δ	108800 = 28 · 52 · 17	Discriminant
Eigenvalues	2-  0 5+  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-143,658]	[a1,a2,a3,a4,a6]
Generators	[-11:30:1]	Generators of the group modulo torsion
j	1263257424/425	j-invariant
L	2.0532909813083	L(r)(E,1)/r!
Ω	3.2750305235369	Real period
R	1.2539064699103	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	1360a1 5440h1 6120k1 3400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680a1

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 680a1

-4	8	-3	5	-7	-11	13	17
1360a1	5440h1	6120k1	3400a1	33320q1	82280a1	114920f1	11560j1

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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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