Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5- 13-	Signs for the Atkin-Lehner involutions
Class	4225k	Isogeny class
Conductor	4225	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4291015625 = 59 · 133	Discriminant
Eigenvalues	1 -2 5-  0 -2 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8701,-313077]	[a1,a2,a3,a4,a6]
Generators	[55028:1576329:64]	Generators of the group modulo torsion
j	16974593	j-invariant
L	2.9133254189981	L(r)(E,1)/r!
Ω	0.49432750636068	Real period
R	5.893512664198	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67600dh2 38025cu2 4225m2 4225n2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225k2

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
1	-2	-	0	-2	-	0	6	6	-6	6	6	-8	-6	-8	12	2	6	-12	-2	6	0	-4	-8	6

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Quadratic twists for elliptic curve 4225k2

-4	-3	5	13
67600dh2	38025cu2	4225m2	4225n2

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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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