Properties

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

Related objects

Downloads

Learn more

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 \([0, 0, 1, 3993, 18301]\) \(45056/27\) \(-4219225854723\) \([]\) \(3168\) \(1.1118\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1089.k1 has rank \(1\).

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