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	16	Product of Tamagawa factors cp
Δ	576650390625 = 310 · 510	Discriminant
Eigenvalues	-1 3- 5+  0  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2255,19622]	[a1,a2,a3,a4,a6]
j	111284641/50625	j-invariant
L	0.82429593904394	L(r)(E,1)/r!
Ω	0.82429593904394	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3600bf3 14400y4 75b3 45a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225c4

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 225c4

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bf3	14400y4	75b3	45a4	11025z3	27225bi3	38025bc3	65025bn3	81225z3	119025be3

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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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