Properties

Label 40310.p
Number of curves 2
Conductor 40310
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("40310.p1")
sage: E.isogeny_class()

Elliptic curves in class 40310.p

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
40310.p1 40310bd2 [1, -1, 1, -310196027862, -66496985128639551] 1 206524416  
40310.p2 40310bd1 [1, -1, 1, -99013362, -835939931151] 7 29503488 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 40310.p have rank \(0\).

Modular form 40310.2.a.p

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.