Properties

Label 134640ci
Number of curves 2
Conductor 134640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("134640.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 134640ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
134640.bw2 134640ci1 [0, 0, 0, -126723, 7646978] [2] 1032192 \(\Gamma_0(N)\)-optimal
134640.bw1 134640ci2 [0, 0, 0, -1693443, 847722242] [2] 2064384  

Rank

sage: E.rank()
 

The elliptic curves in class 134640ci have rank \(1\).

Modular form 134640.2.a.bw

sage: E.q_eigenform(10)
 
\( q - q^{5} + 2q^{7} - q^{11} - 4q^{13} - q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.