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	6720n	Isogeny class
Conductor	6720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1180139520 = 215 · 3 · 5 · 74	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-705,-6783]	[a1,a2,a3,a4,a6]
Generators	[-13:4:1]	Generators of the group modulo torsion
j	1184287112/36015	j-invariant
L	3.5311781669526	L(r)(E,1)/r!
Ω	0.92813060970221	Real period
R	1.9023067066421	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	6720z4 3360t2 20160bs4 33600cm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720n3

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	-2	4	0	6	8	-6	6	8	4	2	0	-10	-8	0	-10	-4	4	-10	-18

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Quadratic twists for elliptic curve 6720n3

-4	8	-3	5	-7
6720z4	3360t2	20160bs4	33600cm3	47040cq3

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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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