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	680b	Isogeny class
Conductor	680	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-174080 = -1 · 211 · 5 · 17	Discriminant
Eigenvalues	2- -1 5-  2  4 -1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,0,-20]	[a1,a2,a3,a4,a6]
j	-2/85	j-invariant
L	1.4663778906941	L(r)(E,1)/r!
Ω	1.4663778906941	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1360b1 5440b1 6120e1 3400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680b1

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
-	-1	-	2	4	-1	-	-1	6	-5	3	4	6	10	5	-3	3	5	-6	-9	13	8	-8	-1	-1

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Quadratic twists for elliptic curve 680b1

-4	8	-3	5	-7	-11	13	17
1360b1	5440b1	6120e1	3400b1	33320i1	82280g1	114920b1	11560d1

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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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