Properties

Label 55.a
Number of curves 4
Conductor 55
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("55.a1")
sage: E.isogeny_class()

Elliptic curves in class 55.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
55.a1 55a3 [1, -1, 0, -59, 190] 4 4  
55.a2 55a2 [1, -1, 0, -29, -52] 2 4  
55.a3 55a1 [1, -1, 0, -4, 3] 4 2 \(\Gamma_0(N)\)-optimal
55.a4 55a4 [1, -1, 0, 1, 0] 2 4  

Rank

sage: E.rank()

The elliptic curves in class 55.a have rank \(0\).

Modular form 55.2.a.a

sage: E.q_eigenform(10)
\( q + q^{2} - q^{4} + q^{5} - 3q^{8} - 3q^{9} + q^{10} - q^{11} + 2q^{13} - q^{16} + 6q^{17} - 3q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.