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	58080f	Isogeny class
Conductor	58080	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	245760	Modular degree for the optimal curve
Δ	51658718760000 = 26 · 36 · 54 · 116	Discriminant
Eigenvalues	2+ 3+ 5+  4 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-27386,-1700664]	[a1,a2,a3,a4,a6]
j	20034997696/455625	j-invariant
L	0.74327133866654	L(r)(E,1)/r!
Ω	0.3716356701091	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	58080cb1 116160et2 480e1	Quadratic twists by: -4 8 -11

Hecke Eigenvalues for elliptic curve 58080f1

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	-	-6	-2	-4	0	-10	-4	-10	-2	4	8	2	12	10	12	0	-10	4	-4	-6	-14

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Quadratic twists for elliptic curve 58080f1

-4	8	-11
58080cb1	116160et2	480e1

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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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