Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Class	4225a	Isogeny class
Conductor	4225	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	1568712925 = 52 · 137	Discriminant
Eigenvalues	0 -1 5+ -4  6 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-563,4968]	[a1,a2,a3,a4,a6]
Generators	[-4:84:1]	Generators of the group modulo torsion
j	163840/13	j-invariant
L	2.1051770890247	L(r)(E,1)/r!
Ω	1.4702288338702	Real period
R	0.71593517979208	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	67600bs1 38025ba1 4225h1 325b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225a1

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
0	-1	+	-4	6	+	-6	4	-3	-3	4	2	-6	7	0	9	6	-1	14	6	-4	11	-6	0	-10

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Quadratic twists for elliptic curve 4225a1

-4	-3	5	13
67600bs1	38025ba1	4225h1	325b1

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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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