Properties

Label 167334.e
Number of curves 2
Conductor 167334
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("167334.e1")
sage: E.isogeny_class()

Elliptic curves in class 167334.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
167334.e1 167334h2 [1, 0, 1, -3472762, 2483879540] 2 8031744  
167334.e2 167334h1 [1, 0, 1, -126082, 71592596] 2 4015872 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 167334.e have rank \(1\).

Modular form None

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

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 LMFDB 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 LMFDB labels.