Cremona's table of elliptic curves

9225 = 3² · 5² · 41

Field	Data	Notes
Atkin-Lehner	3- 5+ 41+	Signs for the Atkin-Lehner involutions
Class	9225p	Isogeny class
Conductor	9225	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-20175075 = -1 · 39 · 52 · 41	Discriminant
Eigenvalues	-1 3- 5+ -2 -3 -2 -7 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,40,182]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1] [0:13:1]	Generators of the group modulo torsion
j	397535/1107	j-invariant
L	3.7598036929057	L(r)(E,1)/r!
Ω	1.518287443109	Real period
R	0.61908627874981	Regulator
r	2	Rank of the group of rational points
S	0.99999999999949	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3075k1 9225ba1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 9225p1

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	-	+	-2	-3	-2	-7	-6	2	2	-9	-6	+	-5	1	1	-6	-7	2	-1	-9	-8	6	17	-10

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Quadratic twists for elliptic curve 9225p1

-3	5
3075k1	9225ba1

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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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