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	1680s	Isogeny class
Conductor	1680	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	680400 = 24 · 35 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5- 7+  2  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-565,-5362]	[a1,a2,a3,a4,a6]
j	1248870793216/42525	j-invariant
L	2.4477344618135	L(r)(E,1)/r!
Ω	0.97909378472538	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	420b1 6720bf1 5040be1 8400bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680s1

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

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Quadratic twists for elliptic curve 1680s1

-4	8	-3	5	-7
420b1	6720bf1	5040be1	8400bn1	11760bn1

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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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