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	6720d	Isogeny class
Conductor	6720	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1290240000 = 215 · 32 · 54 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2721,55521]	[a1,a2,a3,a4,a6]
Generators	[33:24:1]	Generators of the group modulo torsion
j	68017239368/39375	j-invariant
L	3.2763049153178	L(r)(E,1)/r!
Ω	1.5109339788664	Real period
R	0.54209928447304	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	6720v3 3360m3 20160cc3 33600cz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720d4

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

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Quadratic twists for elliptic curve 6720d4

-4	8	-3	5	-7
6720v3	3360m3	20160cc3	33600cz4	47040dk4

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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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