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	6720by	Isogeny class
Conductor	6720	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-285768000 = -1 · 26 · 36 · 53 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7-  2  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,104,-670]	[a1,a2,a3,a4,a6]
j	1925134784/4465125	j-invariant
L	2.6930497330122	L(r)(E,1)/r!
Ω	0.89768324433741	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720be1 3360h2 20160fc1 33600ej1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720by1

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

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Quadratic twists for elliptic curve 6720by1

-4	8	-3	5	-7
6720be1	3360h2	20160fc1	33600ej1	47040fe1

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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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