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	6720bn	Isogeny class
Conductor	6720	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	4515840000 = 214 · 32 · 54 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-945,11025]	[a1,a2,a3,a4,a6]
Generators	[0:105:1]	Generators of the group modulo torsion
j	5702413264/275625	j-invariant
L	3.6784986895124	L(r)(E,1)/r!
Ω	1.3607205492416	Real period
R	0.67583654328632	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	6720bc2 1680e2 20160do2 33600gk2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bn2

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

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Quadratic twists for elliptic curve 6720bn2

-4	8	-3	5	-7
6720bc2	1680e2	20160do2	33600gk2	47040fv2

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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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