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	6720x	Isogeny class
Conductor	6720	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	153090000000000 = 210 · 37 · 510 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7+ -2 -4  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16245,524475]	[a1,a2,a3,a4,a6]
Generators	[-90:1125:1]	Generators of the group modulo torsion
j	463030539649024/149501953125	j-invariant
L	4.8845650519629	L(r)(E,1)/r!
Ω	0.53317133853843	Real period
R	0.26175263259129	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	6720br1 420a1 20160bb1 33600v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720x1

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

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Quadratic twists for elliptic curve 6720x1

-4	8	-3	5	-7
6720br1	420a1	20160bb1	33600v1	47040i1

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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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