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	6720u	Isogeny class
Conductor	6720	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	90672479600640 = 220 · 3 · 5 · 78	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-23681,1317855]	[a1,a2,a3,a4,a6]
Generators	[-21:1344:1]	Generators of the group modulo torsion
j	5602762882081/345888060	j-invariant
L	4.6634928913903	L(r)(E,1)/r!
Ω	0.59304424724246	Real period
R	0.9829563546638	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	6720bg3 210c4 20160cm3 33600l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720u4

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

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Quadratic twists for elliptic curve 6720u4

-4	8	-3	5	-7
6720bg3	210c4	20160cm3	33600l3	47040bq3

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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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