Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5- 13-	Signs for the Atkin-Lehner involutions
Class	4225n	Isogeny class
Conductor	4225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	24960	Modular degree for the optimal curve
Δ	20711912837890625 = 59 · 139	Discriminant
Eigenvalues	-1 -2 5-  0  2 13-  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-97263,-9408608]	[a1,a2,a3,a4,a6]
Generators	[-177:1595:1]	Generators of the group modulo torsion
j	4913	j-invariant
L	1.5279094607316	L(r)(E,1)/r!
Ω	0.2742035647778	Real period
R	5.5721721268275	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	67600di1 38025cs1 4225j1 4225k1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225n1

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 4225n1

-4	-3	5	13
67600di1	38025cs1	4225j1	4225k1

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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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