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	1680h	Isogeny class
Conductor	1680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-265642030080 = -1 · 210 · 32 · 5 · 78	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,160,-24732]	[a1,a2,a3,a4,a6]
Generators	[43:252:1]	Generators of the group modulo torsion
j	439608956/259416045	j-invariant
L	3.3091374215921	L(r)(E,1)/r!
Ω	0.45840412452636	Real period
R	3.6094106101371	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	840g4 6720bh4 5040i4 8400j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680h4

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

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Quadratic twists for elliptic curve 1680h4

-4	8	-3	5	-7
840g4	6720bh4	5040i4	8400j4	11760f4

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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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