Properties

Label 15918w
Number of curves 2
Conductor 15918
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("15918.w1")
sage: E.isogeny_class()

Elliptic curves in class 15918w

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
15918.w2 15918w1 [1, 0, 0, 110624, 15558272] 7 164640 \(\Gamma_0(N)\)-optimal
15918.w1 15918w2 [1, 0, 0, -37076386, -86899858498] 1 1152480  

Rank

sage: E.rank()

The elliptic curves in class 15918w have rank \(1\).

Modular form 15918.2.a.w

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.