Properties

Label 363726j
Number of curves 2
Conductor 363726
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("363726.j1")
sage: E.isogeny_class()

Elliptic curves in class 363726j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
363726.j2 363726j1 [1, -1, 0, -4923, -551259] 2 1474560 \(\Gamma_0(N)\)-optimal*
363726.j1 363726j2 [1, -1, 0, -135603, -19133955] 2 2949120 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 270000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 363726j1.

Rank

sage: E.rank()

The elliptic curves in class 363726j have rank \(0\).

Modular form None

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} - 2q^{5} + 4q^{7} - q^{8} + 2q^{10} - 4q^{14} + q^{16} - 4q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.