Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3- 11-	Signs for the Atkin-Lehner involutions
Class	1089h	Isogeny class
Conductor	1089	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-10673289 = -1 · 36 · 114	Discriminant
Eigenvalues	-1 3- -1 -2 11-  1  5  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-23,168]	[a1,a2,a3,a4,a6]
Generators	[14:42:1]	Generators of the group modulo torsion
j	-121	j-invariant
L	1.5555171297603	L(r)(E,1)/r!
Ω	1.9527584900432	Real period
R	0.1327623750105	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	17424bt1 69696bq1 121c1 27225bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089h1

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	-	1	5	6	-2	-9	-2	-3	5	0	-2	-9	-8	6	2	-12	-2	-10	-6	9	-13

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Quadratic twists for elliptic curve 1089h1

-4	8	-3	5	-7	-11
17424bt1	69696bq1	121c1	27225bj1	53361bm1	1089f2

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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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