Cremona's table of elliptic curves

225 = 3² · 5²

Field	Data	Notes
Atkin-Lehner	3- 5+	Signs for the Atkin-Lehner involutions
Class	225c	Isogeny class
Conductor	225	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2451645281953125 = -1 · 322 · 57	Discriminant
Eigenvalues	-1 3- 5+  0  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-24755,2820872]	[a1,a2,a3,a4,a6]
j	-147281603041/215233605	j-invariant
L	0.82429593904394	L(r)(E,1)/r!
Ω	0.41214796952197	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3600bf8 14400y8 75b8 45a8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225c8

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	-	+	0	4	2	2	4	0	2	0	10	-10	-4	8	-10	4	-2	-12	8	-10	0	12	6	-2

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Quadratic twists for elliptic curve 225c8

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bf8	14400y8	75b8	45a8	11025z8	27225bi7	38025bc7	65025bn7	81225z7	119025be7

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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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