Cremona's table of elliptic curves

10580 = 2² · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	10580d	Isogeny class
Conductor	10580	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	677120 = 28 · 5 · 232	Discriminant
Eigenvalues	2-  2 5+  2  1 -2 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-61,201]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	188416/5	j-invariant
L	6.1548605188377	L(r)(E,1)/r!
Ω	2.8601317085298	Real period
R	0.71731667700033	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42320p1 95220w1 52900p1 10580k1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 10580d1

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	1	-2	-6	-5	-	2	5	10	-3	0	8	-4	4	-9	-8	1	-4	5	-8	6	8

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Quadratic twists for elliptic curve 10580d1

-4	-3	5	-23
42320p1	95220w1	52900p1	10580k1

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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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