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	1868347265625 = 314 · 58	Discriminant
Eigenvalues	-1 3- 5+  0  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-30380,2044622]	[a1,a2,a3,a4,a6]
j	272223782641/164025	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	3600bf5 14400y5 75b5 45a5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225c5

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 225c5

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bf5	14400y5	75b5	45a5	11025z5	27225bi6	38025bc6	65025bn6	81225z6	119025be6

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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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