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	32	Product of Tamagawa factors cp
Δ	2588774400 = 212 · 32 · 52 · 532	Discriminant
Eigenvalues	2- 3- 5+ -4  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-856,9044]	[a1,a2,a3,a4,a6]
Generators	[-26:120:1]	Generators of the group modulo torsion
j	16954786009/632025	j-invariant
L	4.6579524530809	L(r)(E,1)/r!
Ω	1.4315949991561	Real period
R	1.6268401523569	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	795a2 50880dd2 38160ck2 63600cd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12720z2

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 12720z2

-4	8	-3	5
795a2	50880dd2	38160ck2	63600cd2

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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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