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	6720b	Isogeny class
Conductor	6720	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-36126720 = -1 · 214 · 32 · 5 · 72	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -2 -4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,79,81]	[a1,a2,a3,a4,a6]
Generators	[5:24:1]	Generators of the group modulo torsion
j	3286064/2205	j-invariant
L	2.9163872472737	L(r)(E,1)/r!
Ω	1.2945317327105	Real period
R	0.56321277678672	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	6720bz2 420d2 20160by2 33600cx2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720b2

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

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Quadratic twists for elliptic curve 6720b2

-4	8	-3	5	-7
6720bz2	420d2	20160by2	33600cx2	47040di2

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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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