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Properties

Label 1089f
Number of curves $2$
Conductor $1089$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1089f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1089.i2 1089f1 [1, -1, 0, -270, 1777] [] 144 \(\Gamma_0(N)\)-optimal
1089.i1 1089f2 [1, -1, 0, -2745, -215726] [] 1584  

Rank

sage: E.rank()
 

The elliptic curves in class 1089f have rank \(1\).

Complex multiplication

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

Modular form 1089.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - q^{5} + 2q^{7} - 3q^{8} - q^{10} - q^{13} + 2q^{14} - q^{16} - 5q^{17} - 6q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.