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	6720cl	Isogeny class
Conductor	6720	Conductor
∏ cp	960	Product of Tamagawa factors cp
Δ	71137851402240000 = 214 · 310 · 54 · 76	Discriminant
Eigenvalues	2- 3- 5- 7-  0 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-124465,10957775]	[a1,a2,a3,a4,a6]
Generators	[-265:5040:1]	Generators of the group modulo torsion
j	13015144447800784/4341909875625	j-invariant
L	5.1944694421425	L(r)(E,1)/r!
Ω	0.31888351506331	Real period
R	0.27149252505319	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	6720i2 1680b2 20160ea2 33600ee2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720cl2

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

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Quadratic twists for elliptic curve 6720cl2

-4	8	-3	5	-7
6720i2	1680b2	20160ea2	33600ee2	47040ef2

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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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