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	6720cb	Isogeny class
Conductor	6720	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	215040	Modular degree for the optimal curve
Δ	6405501887389080000 = 26 · 328 · 54 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7-  4  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1600156,768989294]	[a1,a2,a3,a4,a6]
j	7079962908642659949376/100085966990454375	j-invariant
L	3.3395860081603	L(r)(E,1)/r!
Ω	0.23854185772574	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720bi1 3360q2 20160fi1 33600eo1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720cb1

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	6	6	4	-4	2	8	-6	6	-8	0	-6	4	-10	-8	12	-14	-16	12	14	18

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Quadratic twists for elliptic curve 6720cb1

-4	8	-3	5	-7
6720bi1	3360q2	20160fi1	33600eo1	47040fk1

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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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