Cremona's table of elliptic curves

9075 = 3 · 5² · 11²

Field	Data	Notes
Atkin-Lehner	3- 5- 11+	Signs for the Atkin-Lehner involutions
Class	9075r	Isogeny class
Conductor	9075	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-1137069140625 = -1 · 37 · 58 · 113	Discriminant
Eigenvalues	-1 3- 5-  1 11+ -2  3  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3638,98517]	[a1,a2,a3,a4,a6]
Generators	[-23:424:1]	Generators of the group modulo torsion
j	-10241915/2187	j-invariant
L	3.4749839520916	L(r)(E,1)/r!
Ω	0.8311690453776	Real period
R	0.099543785473207	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27225bt1 9075a1 9075p1	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 9075r1

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	-	-	1	+	-2	3	3	1	-6	2	-3	-3	-12	-1	-6	-3	10	-6	-7	-2	-7	6	-14	3

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Quadratic twists for elliptic curve 9075r1

-3	5	-11
27225bt1	9075a1	9075p1

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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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