Properties

Label 55545.p
Number of curves 2
Conductor 55545
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55545.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.p1 55545r1 [0, 1, 1, -11285, -1431244] [] 228096 \(\Gamma_0(N)\)-optimal
55545.p2 55545r2 [0, 1, 1, 99805, 34972949] [] 684288  

Rank

sage: E.rank()
 

The elliptic curves in class 55545.p have rank \(0\).

Modular form 55545.2.a.p

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{4} + q^{5} - q^{7} + q^{9} - 3q^{11} - 2q^{12} - 4q^{13} + q^{15} + 4q^{16} + 6q^{17} + q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.