Properties

Label 1089.a
Number of curves $1$
Conductor $1089$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1089.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.a1 1089k1 \([0, 0, 1, 33, -14]\) \(45056/27\) \(-2381643\) \([]\) \(288\) \(-0.087104\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1089.a1 has rank \(1\).

Complex multiplication

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

Modular form 1089.2.a.a

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