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	4	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	4902227890625 = 57 · 137	Discriminant
Eigenvalues	-1  2 5+ -4 -2 13+ -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4313,21406]	[a1,a2,a3,a4,a6]
Generators	[-4:198:1]	Generators of the group modulo torsion
j	117649/65	j-invariant
L	2.8316116615248	L(r)(E,1)/r!
Ω	0.66766080155497	Real period
R	4.2410931642684	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	67600ce1 38025bh1 845a1 325c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 4225b1

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 4225b1

-4	-3	5	13
67600ce1	38025bh1	845a1	325c1

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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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