Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("46410.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46410s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.n4 46410s1 [1, 1, 0, -5427, -3219] [2] 110592 \(\Gamma_0(N)\)-optimal
46410.n2 46410s2 [1, 1, 0, -59507, 5545389] [2, 2] 221184  
46410.n3 46410s3 [1, 1, 0, -32987, 10547061] [2] 442368  
46410.n1 46410s4 [1, 1, 0, -951307, 356736229] [2] 442368  

Rank

sage: E.rank()
 

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

Modular form 46410.2.a.n

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.