Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5- 13-	Signs for the Atkin-Lehner involutions
Class	4225m	Isogeny class
Conductor	4225	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	274625 = 53 · 133	Discriminant
Eigenvalues	-1  2 5-  0 -2 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-348,-2644]	[a1,a2,a3,a4,a6]
Generators	[135:1492:1]	Generators of the group modulo torsion
j	16974593	j-invariant
L	3.2029663448034	L(r)(E,1)/r!
Ω	1.1053499073704	Real period
R	2.8976944978654	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	67600dl2 38025cr2 4225k2 4225j2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225m2

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 4225m2

-4	-3	5	13
67600dl2	38025cr2	4225k2	4225j2

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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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