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	6720x	Isogeny class
Conductor	6720	Conductor
∏ cp	560	Product of Tamagawa factors cp
Δ	-11999512627200000 = -1 · 214 · 314 · 55 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+ -2 -4  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,46255,3636975]	[a1,a2,a3,a4,a6]
Generators	[415:-9720:1]	Generators of the group modulo torsion
j	667990736021936/732392128125	j-invariant
L	4.8845650519629	L(r)(E,1)/r!
Ω	0.26658566926922	Real period
R	0.13087631629564	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	6720br2 420a2 20160bb2 33600v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720x2

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
+	-	-	+	-2	-4	6	-6	-8	2	10	-2	10	4	-8	-4	8	-6	-12	-6	-12	-8	4	-10	8

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Quadratic twists for elliptic curve 6720x2

-4	8	-3	5	-7
6720br2	420a2	20160bb2	33600v2	47040i2

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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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