Properties

Label 118.c
Number of curves 2
Conductor 118
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("118.c1")
sage: E.isogeny_class()

Elliptic curves in class 118.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
118.c1 118b1 [1, 1, 1, -25, 39] 5 12 \(\Gamma_0(N)\)-optimal
118.c2 118b2 [1, 1, 1, 115, -2481] 1 60  

Rank

sage: E.rank()

The elliptic curves in class 118.c have rank \(0\).

Modular form 118.2.a.c

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + q^{10} + 2q^{11} - q^{12} - 6q^{13} + 3q^{14} - q^{15} + q^{16} - 2q^{17} - 2q^{18} - 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.