Properties

Label 5577.a
Number of curves 4
Conductor 5577
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5577.a1")
sage: E.isogeny_class()

Elliptic curves in class 5577.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
5577.a1 5577d3 [1, 1, 1, -24762, 1487988] 2 13824  
5577.a2 5577d2 [1, 1, 1, -1947, 9576] 4 6912  
5577.a3 5577d1 [1, 1, 1, -1102, -14422] 2 3456 \(\Gamma_0(N)\)-optimal
5577.a4 5577d4 [1, 1, 1, 7348, 83936] 2 13824  

Rank

sage: E.rank()

The elliptic curves in class 5577.a have rank \(1\).

Modular form 5577.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.