Properties

Label 46410.m
Number of curves 2
Conductor 46410
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46410.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46410.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.m1 46410m2 [1, 1, 0, -156207, 23697189] [2] 276480  
46410.m2 46410m1 [1, 1, 0, -9327, 402021] [2] 138240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46410.m have rank \(1\).

Modular form 46410.2.a.m

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

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.