Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3- 11-	Signs for the Atkin-Lehner involutions
Class	1089j	Isogeny class
Conductor	1089	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-207992207875419 = -1 · 36 · 1111	Discriminant
Eigenvalues	-2 3- -1  2 11- -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-11253,-832208]	[a1,a2,a3,a4,a6]
Generators	[1474:14637:8]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	1.3531754239545	L(r)(E,1)/r!
Ω	0.22094098060615	Real period
R	1.5311503328198	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	17424bv2 69696bp2 121d2 27225bq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089j2

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	-	-1	2	-	-4	-2	0	1	0	7	3	-8	6	-8	6	-5	-12	-7	3	-4	10	-6	-15	-7

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Quadratic twists for elliptic curve 1089j2

-4	8	-3	5	-7	-11
17424bv2	69696bp2	121d2	27225bq2	53361ca2	99d2

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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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