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	6720o	Isogeny class
Conductor	6720	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	16464000000 = 210 · 3 · 56 · 73	Discriminant
Eigenvalues	2+ 3+ 5- 7- -6  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1205,-14475]	[a1,a2,a3,a4,a6]
Generators	[-20:35:1]	Generators of the group modulo torsion
j	189123395584/16078125	j-invariant
L	3.7533113189875	L(r)(E,1)/r!
Ω	0.81464410417664	Real period
R	0.51192243196815	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	6720cj3 420c3 20160bv3 33600cp3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720o3

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
+	+	-	-	-6	4	6	-2	0	-6	-10	-2	-6	4	0	12	0	-14	4	6	-4	-16	12	6	-16

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Quadratic twists for elliptic curve 6720o3

-4	8	-3	5	-7
6720cj3	420c3	20160bv3	33600cp3	47040cu3

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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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