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	10580f	Isogeny class
Conductor	10580	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	132480	Modular degree for the optimal curve
Δ	-18011526614630000 = -1 · 24 · 54 · 239	Discriminant
Eigenvalues	2- -3 5+  2  2 -1  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,12167,-6436343]	[a1,a2,a3,a4,a6]
Generators	[529:12167:1]	Generators of the group modulo torsion
j	6912/625	j-invariant
L	2.9135475141509	L(r)(E,1)/r!
Ω	0.18439359730023	Real period
R	1.3167248198099	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	42320r1 95220x1 52900t1 10580o1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 10580f1

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	2	-1	6	8	-	-3	-7	-6	-9	-4	-7	12	-4	4	-2	-15	9	0	14	-8	-14

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Quadratic twists for elliptic curve 10580f1

-4	-3	5	-23
42320r1	95220x1	52900t1	10580o1

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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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