Cremona's table of elliptic curves

4225 = 5² · 13²

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Class	4225b	Isogeny class
Conductor	4225	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-318644812890625 = -1 · 58 · 138	Discriminant
Eigenvalues	-1  2 5+ -4 -2 13+ -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,16812,190406]	[a1,a2,a3,a4,a6]
Generators	[1890:81442:1]	Generators of the group modulo torsion
j	6967871/4225	j-invariant
L	2.8316116615248	L(r)(E,1)/r!
Ω	0.33383040077749	Real period
R	2.1205465821342	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	67600ce2 38025bh2 845a2 325c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225b2

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	+	-4	-2	+	-2	6	6	2	10	-2	6	-10	4	-2	-6	2	-4	-6	-6	-12	-16	-2	-2

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Quadratic twists for elliptic curve 4225b2

-4	-3	5	13
67600ce2	38025bh2	845a2	325c2

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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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