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	6720w	Isogeny class
Conductor	6720	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	79659417600 = 214 · 34 · 52 · 74	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2961,59535]	[a1,a2,a3,a4,a6]
Generators	[-21:336:1]	Generators of the group modulo torsion
j	175293437776/4862025	j-invariant
L	4.5736757005992	L(r)(E,1)/r!
Ω	1.0804457527462	Real period
R	0.52914221849805	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	6720bh2 840g2 20160cn2 33600m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720w2

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

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Quadratic twists for elliptic curve 6720w2

-4	8	-3	5	-7
6720bh2	840g2	20160cn2	33600m2	47040br2

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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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