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	1680d	Isogeny class
Conductor	1680	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-3674160 = -1 · 24 · 38 · 5 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15,-90]	[a1,a2,a3,a4,a6]
Generators	[354:1144:27]	Generators of the group modulo torsion
j	-24918016/229635	j-invariant
L	2.620533935913	L(r)(E,1)/r!
Ω	1.0545856242118	Real period
R	4.9697888454939	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	840j1 6720ca1 5040l1 8400w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680d1

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

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Quadratic twists for elliptic curve 1680d1

-4	8	-3	5	-7
840j1	6720ca1	5040l1	8400w1	11760y1

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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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