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	6720r	Isogeny class
Conductor	6720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	258048000 = 215 · 32 · 53 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -4  2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-336001,-75077185]	[a1,a2,a3,a4,a6]
j	128025588102048008/7875	j-invariant
L	1.5863692810964	L(r)(E,1)/r!
Ω	0.19829616013705	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	6720h4 3360f2 20160ca4 33600bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720r3

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	-8	0	2	0	6	2	-4	8	6	0	2	-4	4	-2	4	12	18	6

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Quadratic twists for elliptic curve 6720r3

-4	8	-3	5	-7
6720h4	3360f2	20160ca4	33600bc4	47040bp4

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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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