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
Δ	265112484325 = 52 · 139	Discriminant
Eigenvalues	0 -1 5+ -4  6 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-9013,-325427]	[a1,a2,a3,a4,a6]
Generators	[-422:165:8]	Generators of the group modulo torsion
j	671088640/2197	j-invariant
L	2.1051770890247	L(r)(E,1)/r!
Ω	0.49007627795673	Real period
R	2.1478055393762	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	67600bs2 38025ba2 4225h2 325b2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225a2

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 4225a2

-4	-3	5	13
67600bs2	38025ba2	4225h2	325b2

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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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