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	1680g	Isogeny class
Conductor	1680	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	914457600 = 210 · 36 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-336,1764]	[a1,a2,a3,a4,a6]
Generators	[-6:60:1]	Generators of the group modulo torsion
j	4108974916/893025	j-invariant
L	3.1592013196856	L(r)(E,1)/r!
Ω	1.4852930043568	Real period
R	0.35449810356372	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	840a2 6720bt2 5040r2 8400d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680g2

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

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Quadratic twists for elliptic curve 1680g2

-4	8	-3	5	-7
840a2	6720bt2	5040r2	8400d2	11760q2

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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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