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	6720g	Isogeny class
Conductor	6720	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3440640000 = 218 · 3 · 54 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0  6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7201,-232799]	[a1,a2,a3,a4,a6]
j	157551496201/13125	j-invariant
L	2.0730438491334	L(r)(E,1)/r!
Ω	0.51826096228335	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6720bx3 105a3 20160ch3 33600ce4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720g3

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	6	2	8	8	2	4	2	-6	-4	8	-10	-4	2	-4	-12	-2	8	4	-6	-18

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Quadratic twists for elliptic curve 6720g3

-4	8	-3	5	-7
6720bx3	105a3	20160ch3	33600ce4	47040df4

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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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