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	1680m	Isogeny class
Conductor	1680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1469506208767672320 = -1 · 218 · 34 · 5 · 712	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-325640,92398320]	[a1,a2,a3,a4,a6]
Generators	[842:20358:1]	Generators of the group modulo torsion
j	-932348627918877961/358766164249920	j-invariant
L	2.5723360911699	L(r)(E,1)/r!
Ω	0.25272506696916	Real period
R	5.0891985548148	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	210b8 6720bw8 5040bc8 8400cf8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680m8

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

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Quadratic twists for elliptic curve 1680m8

-4	8	-3	5	-7
210b8	6720bw8	5040bc8	8400cf8	11760cd8

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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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