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	12720bl	Isogeny class
Conductor	12720	Conductor
∏ cp	264	Product of Tamagawa factors cp
deg	2090880	Modular degree for the optimal curve
Δ	-1230607613952000000 = -1 · 223 · 311 · 56 · 53	Discriminant
Eigenvalues	2- 3- 5- -5  5 -2  8 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-138698240,628669809588]	[a1,a2,a3,a4,a6]
Generators	[6826:-3840:1]	Generators of the group modulo torsion
j	-72040483310118508805967361/300441312000000	j-invariant
L	5.4619811917549	L(r)(E,1)/r!
Ω	0.18346486857391	Real period
R	0.11276994258825	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1590r1 50880cg1 38160bl1 63600bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720bl1

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
-	-	-	-5	5	-2	8	-3	-5	-5	2	-4	-11	-8	6	-	0	7	-11	-3	-6	0	-2	16	7

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Quadratic twists for elliptic curve 12720bl1

-4	8	-3	5
1590r1	50880cg1	38160bl1	63600bt1

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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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