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	6720be	Isogeny class
Conductor	6720	Conductor
∏ cp	4	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	1.2067221309414	L(r)(E,1)/r!
Ω	1.2067221309414	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	6720by1 3360l2 20160ep1 33600go1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720be1

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 6720be1

-4	8	-3	5	-7
6720by1	3360l2	20160ep1	33600go1	47040ha1

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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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