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
deg	48	Modular degree for the optimal curve
Δ	-170859375 = -1 · 37 · 57	Discriminant
Eigenvalues	-1 3- 5+  0  4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5,-628]	[a1,a2,a3,a4,a6]
j	-1/15	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	3600bf1 14400y1 75b1 45a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 225c1

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 225c1

-4	8	-3	5	-7	-11	13	17	-19	-23
3600bf1	14400y1	75b1	45a1	11025z1	27225bi1	38025bc1	65025bn1	81225z1	119025be1

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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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