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	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	35280 = 24 · 32 · 5 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-735,-7920]	[a1,a2,a3,a4,a6]
Generators	[48:264:1]	Generators of the group modulo torsion
j	2748251600896/2205	j-invariant
L	3.3091374215921	L(r)(E,1)/r!
Ω	0.91680824905271	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	840g1 6720bh1 5040i1 8400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680h1

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 1680h1

-4	8	-3	5	-7
840g1	6720bh1	5040i1	8400j1	11760f1

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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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