Properties

Label 1089g
Number of curves 4
Conductor 1089
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1089.j1")
sage: E.isogeny_class()

Elliptic curves in class 1089g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1089.j3 1089g1 [1, -1, 0, -7101, -226616] 2 1440 \(\Gamma_0(N)\)-optimal
1089.j2 1089g2 [1, -1, 0, -12546, 173047] 4 2880  
1089.j1 1089g3 [1, -1, 0, -159561, 24548134] 2 5760  
1089.j4 1089g4 [1, -1, 0, 47349, 1311052] 2 5760  

Rank

sage: E.rank()

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

Modular form 1089.2.a.j

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.