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	6720k	Isogeny class
Conductor	6720	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4720558080 = 217 · 3 · 5 · 74	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2625,52545]	[a1,a2,a3,a4,a6]
Generators	[32:17:1]	Generators of the group modulo torsion
j	15267472418/36015	j-invariant
L	3.805356619679	L(r)(E,1)/r!
Ω	1.3754370468091	Real period
R	2.7666527003232	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	6720cf3 840i3 20160bm3 33600cb4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6720k3

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	-2	2	-4	0	-2	4	-2	-2	-8	-4	2	-12	14	-8	-8	-2	8	4	-18	-2

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Quadratic twists for elliptic curve 6720k3

-4	8	-3	5	-7
6720cf3	840i3	20160bm3	33600cb4	47040cd4

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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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