Cremona's table of elliptic curves

1089 = 3² · 11²

Field	Data	Notes
Atkin-Lehner	3+ 11-	Signs for the Atkin-Lehner involutions
Class	1089d	Isogeny class
Conductor	1089	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	383565986793 = 39 · 117	Discriminant
Eigenvalues	-1 3+  4  2 11-  2  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1838,-5156]	[a1,a2,a3,a4,a6]
j	19683/11	j-invariant
L	1.5661602678489	L(r)(E,1)/r!
Ω	0.78308013392443	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bh1 69696s1 1089c1 27225h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1089d1

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	2	6	-4	-6	4	-6	-10	-6	8	0	-4	6	8	0	2	10	12	0	2

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Quadratic twists for elliptic curve 1089d1

-4	8	-3	5	-7	-11
17424bh1	69696s1	1089c1	27225h1	53361n1	99c1

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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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