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	4276275200 = 211 · 52 · 174	Discriminant
Eigenvalues	2-  0 5+  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1163,-14938]	[a1,a2,a3,a4,a6]
Generators	[46:170:1]	Generators of the group modulo torsion
j	84944038338/2088025	j-invariant
L	2.0532909813083	L(r)(E,1)/r!
Ω	0.81875763088423	Real period
R	1.2539064699103	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	1360a3 5440h3 6120k3 3400a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680a3

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 680a3

-4	8	-3	5	-7	-11	13	17
1360a3	5440h3	6120k3	3400a3	33320q4	82280a4	114920f4	11560j3

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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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