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	9075s	Isogeny class
Conductor	9075	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	373034693302734375 = 34 · 59 · 119	Discriminant
Eigenvalues	-1 3- 5- -4 11+ -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-856138,-303556483]	[a1,a2,a3,a4,a6]
Generators	[2027:78299:1]	Generators of the group modulo torsion
j	15069223/81	j-invariant
L	2.722598098121	L(r)(E,1)/r!
Ω	0.15700162686842	Real period
R	4.3353023666479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27225bu2 9075h2 9075q2	Quadratic twists by: -3 5 -11

Hecke Eigenvalues for elliptic curve 9075s2

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	-	-	-4	+	-2	-2	8	-4	4	-8	-8	12	8	4	4	-8	0	4	-12	-2	8	-4	6	8

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Quadratic twists for elliptic curve 9075s2

-3	5	-11
27225bu2	9075h2	9075q2

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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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