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	6720bp	Isogeny class
Conductor	6720	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	-10584000000000000 = -1 · 215 · 33 · 512 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+  4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,35615,-4231775]	[a1,a2,a3,a4,a6]
Generators	[120:1325:1]	Generators of the group modulo torsion
j	152461584507448/322998046875	j-invariant
L	3.6902675319359	L(r)(E,1)/r!
Ω	0.21095953863828	Real period
R	2.9154623328532	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	6720cm4 3360i4 20160dx4 33600gs3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bp4

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	-2	0	-4	-2	8	-10	2	-4	4	-10	-4	2	-4	0	-6	8	4	-6	10

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Quadratic twists for elliptic curve 6720bp4

-4	8	-3	5	-7
6720cm4	3360i4	20160dx4	33600gs3	47040ge3

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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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