Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3- 11-	Signs for the Atkin-Lehner involutions
Class	1089i	Isogeny class
Conductor	1089	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	-4219225854723 = -1 · 39 · 118	Discriminant
Eigenvalues	2 3- -4  1 11- -2 -4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,3993,18301]	[a1,a2,a3,a4,a6]
Generators	[242:3263:8]	Generators of the group modulo torsion
j	45056/27	j-invariant
L	3.878780097073	L(r)(E,1)/r!
Ω	0.47680119181379	Real period
R	0.6779170864202	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	17424cj1 69696dm1 363c1 27225br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089i1

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
2	-	-4	1	-	-2	-4	-3	-2	-6	-5	3	2	12	-2	-6	10	3	-1	0	-11	11	-6	-12	5

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Quadratic twists for elliptic curve 1089i1

-4	8	-3	5	-7	-11
17424cj1	69696dm1	363c1	27225br1	53361by1	1089k1

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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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