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	12720z	Isogeny class
Conductor	12720	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	407040000 = 212 · 3 · 54 · 53	Discriminant
Eigenvalues	2- 3- 5+ -4  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13576,604340]	[a1,a2,a3,a4,a6]
Generators	[292:4650:1]	Generators of the group modulo torsion
j	67563360340489/99375	j-invariant
L	4.6579524530809	L(r)(E,1)/r!
Ω	1.4315949991561	Real period
R	3.2536803047137	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	795a3 50880dd4 38160ck4 63600cd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720z3

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	4	-2	-2	-4	8	-10	8	-2	6	0	8	+	-4	-10	12	-12	6	8	-12	-6	18

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Quadratic twists for elliptic curve 12720z3

-4	8	-3	5
795a3	50880dd4	38160ck4	63600cd4

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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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