Cremona's table of elliptic curves

54080 = 2⁶ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	54080db	Isogeny class
Conductor	54080	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	4326400 = 210 · 52 · 132	Discriminant
Eigenvalues	2- -1 5- -3 -5 13+  5  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-225,-1223]	[a1,a2,a3,a4,a6]
Generators	[-8:1:1]	Generators of the group modulo torsion
j	7311616/25	j-invariant
L	3.6770973918876	L(r)(E,1)/r!
Ω	1.2324873902902	Real period
R	1.4917383418266	Regulator
r	1	Rank of the group of rational points
S	1.0000000000164	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54080bg1 13520d1 54080cb1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 54080db1

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
-	-1	-	-3	-5	+	5	1	1	9	-4	-3	1	-3	-8	-10	-3	-7	9	7	-10	16	-12	-15	7

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Quadratic twists for elliptic curve 54080db1

-4	8	13
54080bg1	13520d1	54080cb1

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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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