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	32	Product of Tamagawa factors cp
Δ	45158400 = 212 · 32 · 52 · 72	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-105,297]	[a1,a2,a3,a4,a6]
Generators	[-3:24:1]	Generators of the group modulo torsion
j	31554496/11025	j-invariant
L	3.5311781669526	L(r)(E,1)/r!
Ω	1.8562612194044	Real period
R	0.95115335332104	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6720z2 3360t1 20160bs2 33600cm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720n2

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 6720n2

-4	8	-3	5	-7
6720z2	3360t1	20160bs2	33600cm2	47040cq2

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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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