Cremona's table of elliptic curves

12720 = 2⁴ · 3 · 5 · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 53+	Signs for the Atkin-Lehner involutions
Class	12720w	Isogeny class
Conductor	12720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3.975E+21	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2386856,3348222900]	[a1,a2,a3,a4,a6]
Generators	[-123666115436275692:1935875612441406250:64572901005159]	Generators of the group modulo torsion
j	-367149213333770500009/970458984375000000	j-invariant
L	5.037200843951	L(r)(E,1)/r!
Ω	0.12289846380034	Real period
R	20.493343399858	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	1590a4 50880cv3 38160cd3 63600bx3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720w4

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

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Quadratic twists for elliptic curve 12720w4

-4	8	-3	5
1590a4	50880cv3	38160cd3	63600bx3

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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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