Cremona's table of elliptic curves

58080 = 2⁵ · 3 · 5 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 11-	Signs for the Atkin-Lehner involutions
Class	58080bk	Isogeny class
Conductor	58080	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1198080	Modular degree for the optimal curve
Δ	-2777948395200000000 = -1 · 212 · 315 · 58 · 112	Discriminant
Eigenvalues	2- 3+ 5+ -3 11-  2 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1317741,588163941]	[a1,a2,a3,a4,a6]
Generators	[-889:32500:1]	Generators of the group modulo torsion
j	-510585996566086144/5605041796875	j-invariant
L	3.2580379504875	L(r)(E,1)/r!
Ω	0.25611742221321	Real period
R	3.1802189815983	Regulator
r	1	Rank of the group of rational points
S	0.99999999997717	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58080bz1 116160jk1 58080e1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 58080bk1

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
-	+	+	-3	-	2	-4	-7	-2	6	1	11	-8	-4	-4	-2	-2	5	1	-2	11	11	-16	-2	9

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Quadratic twists for elliptic curve 58080bk1

-4	8	-11
58080bz1	116160jk1	58080e1

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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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