Cremona's table of elliptic curves

22560 = 2⁵ · 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 47-	Signs for the Atkin-Lehner involutions
Class	22560g	Isogeny class
Conductor	22560	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	13312	Modular degree for the optimal curve
Δ	795240000 = 26 · 32 · 54 · 472	Discriminant
Eigenvalues	2+ 3- 5+  4  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-786,-8640]	[a1,a2,a3,a4,a6]
Generators	[242229:2463300:2197]	Generators of the group modulo torsion
j	840163473856/12425625	j-invariant
L	7.050506198622	L(r)(E,1)/r!
Ω	0.90237472685233	Real period
R	7.8132797703849	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22560m1 45120s2 67680ba1 112800bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22560g1

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	0	2	2	-4	-8	2	-8	6	-2	-12	-	-14	4	14	4	-8	-6	-4	-12	-14	18

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Quadratic twists for elliptic curve 22560g1

-4	8	-3	5
22560m1	45120s2	67680ba1	112800bp1

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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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