Properties

Label 46410c
Number of curves 4
Conductor 46410
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46410.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46410c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.b3 46410c1 [1, 1, 0, -71018, -7312812] [2] 172032 \(\Gamma_0(N)\)-optimal
46410.b2 46410c2 [1, 1, 0, -79018, -5573612] [2, 2] 344064  
46410.b4 46410c3 [1, 1, 0, 230382, -38184372] [2] 688128  
46410.b1 46410c4 [1, 1, 0, -516418, 138505948] [2] 688128  

Rank

sage: E.rank()
 

The elliptic curves in class 46410c have rank \(0\).

Modular form 46410.2.a.b

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 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.