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	6720o	Isogeny class
Conductor	6720	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-2168506368000 = -1 · 214 · 32 · 53 · 76	Discriminant
Eigenvalues	2+ 3+ 5- 7- -6  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1295,-68975]	[a1,a2,a3,a4,a6]
Generators	[45:280:1]	Generators of the group modulo torsion
j	14647977776/132355125	j-invariant
L	3.7533113189875	L(r)(E,1)/r!
Ω	0.40732205208832	Real period
R	0.25596121598407	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	6720cj4 420c4 20160bv4 33600cp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720o4

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
+	+	-	-	-6	4	6	-2	0	-6	-10	-2	-6	4	0	12	0	-14	4	6	-4	-16	12	6	-16

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Quadratic twists for elliptic curve 6720o4

-4	8	-3	5	-7
6720cj4	420c4	20160bv4	33600cp4	47040cu4

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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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