Cremona's table of elliptic curves

8580 = 2² · 3 · 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	8580c	Isogeny class
Conductor	8580	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-9266400000 = -1 · 28 · 34 · 55 · 11 · 13	Discriminant
Eigenvalues	2- 3+ 5- -4 11+ 13+ -1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-445,6025]	[a1,a2,a3,a4,a6]
Generators	[-5:90:1]	Generators of the group modulo torsion
j	-38153936896/36196875	j-invariant
L	3.2417386358755	L(r)(E,1)/r!
Ω	1.1833035328352	Real period
R	0.091318881023092	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	34320cj1 25740e1 42900bc1 94380m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 8580c1

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	+	+	-1	-1	6	0	6	-11	11	5	1	-12	6	-10	-7	14	12	10	6	-6	-17

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Quadratic twists for elliptic curve 8580c1

-4	-3	5	-11	13
34320cj1	25740e1	42900bc1	94380m1	111540h1

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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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