Properties

Label 1089.k
Number of curves 11
Conductor 10891089
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 1089.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.k1 1089i1 [0,0,1,3993,18301][0, 0, 1, 3993, 18301] 45056/2745056/27 4219225854723-4219225854723 [][] 31683168 1.11181.1118 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1089.k1 has rank 11.

Complex multiplication

The elliptic curves in class 1089.k do not have complex multiplication.

Modular form 1089.2.a.k

sage: E.q_eigenform(10)
 
q+2q2+2q44q5+q78q102q13+2q144q164q173q19+O(q20)q + 2 q^{2} + 2 q^{4} - 4 q^{5} + q^{7} - 8 q^{10} - 2 q^{13} + 2 q^{14} - 4 q^{16} - 4 q^{17} - 3 q^{19} + O(q^{20}) Copy content Toggle raw display