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	6720cf	Isogeny class
Conductor	6720	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	1720320 = 214 · 3 · 5 · 7	Discriminant
Eigenvalues	2- 3- 5- 7+  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-145,623]	[a1,a2,a3,a4,a6]
j	20720464/105	j-invariant
L	2.6682406312412	L(r)(E,1)/r!
Ω	2.6682406312412	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	6720k1 1680a1 20160dp1 33600ev1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720cf1

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	2	4	0	-2	-4	-2	-2	8	4	2	12	14	8	8	-2	-8	-4	-18	-2

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Quadratic twists for elliptic curve 6720cf1

-4	8	-3	5	-7
6720k1	1680a1	20160dp1	33600ev1	47040ea1

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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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