Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("363726.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 363726.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
363726.j1 363726j2 [1, -1, 0, -135603, -19133955] [2] 2949120  
363726.j2 363726j1 [1, -1, 0, -4923, -551259] [2] 1474560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 363726.2.a.j

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 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.