Properties

Label 345520bn
Number of curves 2
Conductor 345520
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("345520.bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 345520bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
345520.bn2 345520bn1 [0, 0, 0, -2205307, -1279493206] [] 20942208 \(\Gamma_0(N)\)-optimal
345520.bn1 345520bn2 [0, 0, 0, -20332507, 154395929354] [] 146595456  

Rank

sage: E.rank()
 

The elliptic curves in class 345520bn have rank \(0\).

Modular form 345520.2.a.bn

sage: E.q_eigenform(10)
 
\( q + 3q^{3} + q^{5} - q^{7} + 6q^{9} + 2q^{11} - 7q^{13} + 3q^{15} + 4q^{17} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.