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	6720c	Isogeny class
Conductor	6720	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-243524645683200 = -1 · 234 · 34 · 52 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,13439,447361]	[a1,a2,a3,a4,a6]
Generators	[-29:180:1]	Generators of the group modulo torsion
j	1023887723039/928972800	j-invariant
L	3.2776134934885	L(r)(E,1)/r!
Ω	0.36272209421397	Real period
R	2.2590390451616	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720cd1 210e1 20160ce1 33600da1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720c1

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	2	0	-6	-6	4	0	10	-12	-14	12	-8	10	16	12	10	2

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Quadratic twists for elliptic curve 6720c1

-4	8	-3	5	-7
6720cd1	210e1	20160ce1	33600da1	47040dm1

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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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