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	6720m	Isogeny class
Conductor	6720	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-26578125000000 = -1 · 26 · 35 · 512 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7-  4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2940,-254538]	[a1,a2,a3,a4,a6]
Generators	[3082:59675:8]	Generators of the group modulo torsion
j	-43927191786304/415283203125	j-invariant
L	4.0451469615341	L(r)(E,1)/r!
Ω	0.28299113239056	Real period
R	4.7647511394471	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	6720ba1 3360u4 20160bt1 33600ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720m1

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

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Quadratic twists for elliptic curve 6720m1

-4	8	-3	5	-7
6720ba1	3360u4	20160bt1	33600ck1	47040cm1

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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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