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	6720l	Isogeny class
Conductor	6720	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	17348050944000000 = 220 · 32 · 56 · 76	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-172865,-26870463]	[a1,a2,a3,a4,a6]
Generators	[-256:735:1]	Generators of the group modulo torsion
j	2179252305146449/66177562500	j-invariant
L	3.7757685625521	L(r)(E,1)/r!
Ω	0.23457381936662	Real period
R	0.89423841376747	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	6720cg6 210a6 20160bn6 33600cc6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720l6

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
+	+	-	-	0	-2	-6	4	0	6	-4	-2	6	-8	-12	-6	12	-2	-8	0	14	-16	-12	6	14

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Quadratic twists for elliptic curve 6720l6

-4	8	-3	5	-7
6720cg6	210a6	20160bn6	33600cc6	47040cf6

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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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