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	6720bg	Isogeny class
Conductor	6720	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2601123840000 = 220 · 34 · 54 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7+  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-67201,6727201]	[a1,a2,a3,a4,a6]
j	128031684631201/9922500	j-invariant
L	1.5453737168316	L(r)(E,1)/r!
Ω	0.77268685841582	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6720u3 1680t4 20160ev3 33600gt4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720bg4

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 6720bg4

-4	8	-3	5	-7
6720u3	1680t4	20160ev3	33600gt4	47040hc4

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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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