Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Class	4225c	Isogeny class
Conductor	4225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	14112	Modular degree for the optimal curve
Δ	44804009850925 = 52 · 1311	Discriminant
Eigenvalues	2 -1 5+  2 -2 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-16618,764623]	[a1,a2,a3,a4,a6]
Generators	[-9148:28529:64]	Generators of the group modulo torsion
j	4206161920/371293	j-invariant
L	5.9532916615411	L(r)(E,1)/r!
Ω	0.62355641000806	Real period
R	2.3868296300026	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	67600bq1 38025br1 4225i2 325e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225c1

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
2	-1	+	2	-2	+	-2	0	9	5	-2	-8	-12	-1	-8	-11	0	-13	2	-12	6	15	-4	10	-8

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Quadratic twists for elliptic curve 4225c1

-4	-3	5	13
67600bq1	38025br1	4225i2	325e1

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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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