Cremona's table of elliptic curves

225 = 3² · 5²

Field	Data	Notes
Atkin-Lehner	3+ 5+	Signs for the Atkin-Lehner involutions
Class	225a	Isogeny class
Conductor	225	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-675 = -1 · 33 · 52	Discriminant
Eigenvalues	0 3+ 5+ -5  0 -5  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,1]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	0	j-invariant
L	1.2453986750529	L(r)(E,1)/r!
Ω	4.0529757590369	Real period
R	0.15364003501329	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	3600bc1 14400m1 225a2 225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225a1

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
0	+	+	-5	0	-5	0	-1	0	0	-7	10	0	-5	0	0	0	-13	-5	0	10	-4	0	0	-5

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Quadratic twists for elliptic curve 225a1

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bc1	14400m1	225a2	225b1	11025d1	27225b1	38025g1	65025c1	81225e1	119025b1

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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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