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	6720u	Isogeny class
Conductor	6720	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	2601123840000 = 220 · 34 · 54 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-67201,-6727201]	[a1,a2,a3,a4,a6]
Generators	[427:6528:1]	Generators of the group modulo torsion
j	128031684631201/9922500	j-invariant
L	4.6634928913903	L(r)(E,1)/r!
Ω	0.29652212362123	Real period
R	3.9318254186552	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	6720bg4 210c3 20160cm4 33600l4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720u3

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	4	-8	-6	-8	2	2	12	-8	-6	-4	2	-12	8	-14	0	-12	2	10

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Quadratic twists for elliptic curve 6720u3

-4	8	-3	5	-7
6720bg4	210c3	20160cm4	33600l4	47040bq4

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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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