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	54080r	Isogeny class
Conductor	54080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	258048	Modular degree for the optimal curve
Δ	4176541291520 = 210 · 5 · 138	Discriminant
Eigenvalues	2+ -2 5+ -2  4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-190181,31859179]	[a1,a2,a3,a4,a6]
Generators	[-5:5728:1]	Generators of the group modulo torsion
j	153910165504/845	j-invariant
L	3.5465872114939	L(r)(E,1)/r!
Ω	0.69206213462896	Real period
R	5.1246658847987	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	54080cf1 3380h1 4160h1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 54080r1

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
+	-2	+	-2	4	+	2	0	-6	10	0	10	2	-2	6	-2	-8	-2	-6	8	-10	-16	6	-10	-2

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Quadratic twists for elliptic curve 54080r1

-4	8	13
54080cf1	3380h1	4160h1

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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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