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	6720z	Isogeny class
Conductor	6720	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	45158400 = 212 · 32 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+  4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-105,-297]	[a1,a2,a3,a4,a6]
Generators	[-7:12:1]	Generators of the group modulo torsion
j	31554496/11025	j-invariant
L	5.0472840906944	L(r)(E,1)/r!
Ω	1.532949324819	Real period
R	1.6462657991941	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	6720n2 3360d1 20160bi2 33600z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720z2

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	-6	-2	-4	0	6	-8	-6	6	-8	-4	2	0	-10	8	0	-10	4	-4	-10	-18

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Quadratic twists for elliptic curve 6720z2

-4	8	-3	5	-7
6720n2	3360d1	20160bi2	33600z2	47040n2

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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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