Cremona's table of elliptic curves

1680 = 2⁴ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7-	Signs for the Atkin-Lehner involutions
Class	1680b	Isogeny class
Conductor	1680	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1111528928160000 = 28 · 310 · 54 · 76	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31116,1385280]	[a1,a2,a3,a4,a6]
j	13015144447800784/4341909875625	j-invariant
L	1.3529081754592	L(r)(E,1)/r!
Ω	0.45096939181974	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	840d2 6720cl2 5040q2 8400s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680b2

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	6	-2	-4	-4	6	0	6	-2	4	-8	-2	12	6	4	12	10	8	12	14	2

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Quadratic twists for elliptic curve 1680b2

-4	8	-3	5	-7
840d2	6720cl2	5040q2	8400s2	11760bg2

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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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