Properties

Label 110466bp
Number of curves 4
Conductor 110466
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("110466.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 110466bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110466.bi4 110466bp1 [1, -1, 1, -9815, 234159] [2] 331776 \(\Gamma_0(N)\)-optimal
110466.bi3 110466bp2 [1, -1, 1, -139775, 20144031] [2] 663552  
110466.bi2 110466bp3 [1, -1, 1, -334715, -74440857] [2] 995328  
110466.bi1 110466bp4 [1, -1, 1, -367205, -59092581] [2] 1990656  

Rank

sage: E.rank()
 

The elliptic curves in class 110466bp have rank \(1\).

Modular form 110466.2.a.bi

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - 4q^{7} + q^{8} - 6q^{11} - 2q^{13} - 4q^{14} + q^{16} + q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.