Cremona's table of elliptic curves

6720 = 2⁶ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	6720v	Isogeny class
Conductor	6720	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	7524679680 = 215 · 38 · 5 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1601,23775]	[a1,a2,a3,a4,a6]
Generators	[-29:216:1]	Generators of the group modulo torsion
j	13858588808/229635	j-invariant
L	4.6212323136784	L(r)(E,1)/r!
Ω	1.3220540327429	Real period
R	0.43693678541363	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	6720d3 3360o3 20160cl3 33600k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720v4

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

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Quadratic twists for elliptic curve 6720v4

-4	8	-3	5	-7
6720d3	3360o3	20160cl3	33600k3	47040bo3

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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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