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
Δ	-156267624249 = -1 · 36 · 118	Discriminant
Eigenvalues	-1 3- -1 -2 11-  1  5  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-32693,-2267130]	[a1,a2,a3,a4,a6]
Generators	[212:438:1]	Generators of the group modulo torsion
j	-24729001	j-invariant
L	1.5555171297603	L(r)(E,1)/r!
Ω	0.17752349909483	Real period
R	1.4603861251155	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	17424bt2 69696bq2 121c2 27225bj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089h2

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 1089h2

-4	8	-3	5	-7	-11
17424bt2	69696bq2	121c2	27225bj2	53361bm2	1089f1

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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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