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	680c	Isogeny class
Conductor	680	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-115600000000 = -1 · 210 · 58 · 172	Discriminant
Eigenvalues	2-  2 5-  2 -2  2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3520,-80868]	[a1,a2,a3,a4,a6]
j	-4711672753924/112890625	j-invariant
L	2.4757028802046	L(r)(E,1)/r!
Ω	0.30946286002557	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1360c2 5440d2 6120d2 3400d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 680c2

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
-	2	-	2	-2	2	-	8	-6	-2	6	-2	-6	-8	8	6	0	-10	12	6	-14	2	-8	-10	2

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Quadratic twists for elliptic curve 680c2

-4	8	-3	5	-7	-11	13	17
1360c2	5440d2	6120d2	3400d2	33320k2	82280i2	114920c2	11560e2

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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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