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	1680a	Isogeny class
Conductor	1680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-725760000 = -1 · 211 · 34 · 54 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,224,-224]	[a1,a2,a3,a4,a6]
Generators	[10:54:1]	Generators of the group modulo torsion
j	604223422/354375	j-invariant
L	2.3423776590419	L(r)(E,1)/r!
Ω	0.94336552209408	Real period
R	1.24150056589	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	840i4 6720cf4 5040n4 8400y4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680a4

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	2	-4	0	2	-4	2	-2	-8	4	-2	-12	-14	-8	8	-2	-8	4	-18	-2

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Quadratic twists for elliptic curve 1680a4

-4	8	-3	5	-7
840i4	6720cf4	5040n4	8400y4	11760bd4

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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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