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	73758720 = 211 · 3 · 5 · 74	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-656,-6240]	[a1,a2,a3,a4,a6]
Generators	[-14:2:1]	Generators of the group modulo torsion
j	15267472418/36015	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	840i3 6720cf3 5040n3 8400y3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680a3

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 1680a3

-4	8	-3	5	-7
840i3	6720cf3	5040n3	8400y3	11760bd3

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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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