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	2	Product of Tamagawa factors cp
Δ	-13600000000 = -1 · 211 · 58 · 17	Discriminant
Eigenvalues	2-  0 5+  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,517,3318]	[a1,a2,a3,a4,a6]
Generators	[138:1644:1]	Generators of the group modulo torsion
j	7462174302/6640625	j-invariant
L	2.0532909813083	L(r)(E,1)/r!
Ω	0.81875763088423	Real period
R	5.0156258796412	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	1360a4 5440h4 6120k4 3400a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680a4

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 680a4

-4	8	-3	5	-7	-11	13	17
1360a4	5440h4	6120k4	3400a4	33320q3	82280a3	114920f3	11560j4

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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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