Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("55545.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55545l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55545.u1 55545l1 [1, 0, 1, -760449, 254433247] [2] 608256 \(\Gamma_0(N)\)-optimal
55545.u2 55545l2 [1, 0, 1, -429824, 477142247] [2] 1216512  

Rank

sage: E.rank()
 

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

Modular form 55545.2.a.u

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} - q^{10} + 2q^{11} - q^{12} + q^{14} - q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.