Properties

Label 46410.p
Number of curves 4
Conductor 46410
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46410.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46410.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.p1 46410n4 [1, 1, 0, -740012, -245331216] [2] 491520  
46410.p2 46410n3 [1, 1, 0, -90092, 4453296] [2] 491520  
46410.p3 46410n2 [1, 1, 0, -46412, -3819696] [2, 2] 245760  
46410.p4 46410n1 [1, 1, 0, -332, -160944] [2] 122880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 46410.2.a.p

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

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.