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	6720cm	Isogeny class
Conductor	6720	Conductor
∏ cp	576	Product of Tamagawa factors cp
Δ	112021056000000 = 212 · 36 · 56 · 74	Discriminant
Eigenvalues	2- 3- 5- 7- -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17305,707303]	[a1,a2,a3,a4,a6]
Generators	[-79:1260:1]	Generators of the group modulo torsion
j	139927692143296/27348890625	j-invariant
L	5.1175270297231	L(r)(E,1)/r!
Ω	0.56220645586838	Real period
R	0.25284933518568	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	6720bp2 3360e1 20160ef2 33600ep2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720cm2

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 6720cm2

-4	8	-3	5	-7
6720bp2	3360e1	20160ef2	33600ep2	47040eo2

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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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