Properties

Label 250173.bh
Number of curves 4
Conductor 250173
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("250173.bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.bh1 250173bh3 [1, -1, 0, -602606718, 1786486302139] [2] 118702080  
250173.bh2 250173bh2 [1, -1, 0, -341175933, -2405138046080] [2, 2] 59351040  
250173.bh3 250173bh1 [1, -1, 0, -340379928, -2417011415861] [2] 29675520 \(\Gamma_0(N)\)-optimal
250173.bh4 250173bh4 [1, -1, 0, -92481228, -5836876280375] [2] 118702080  

Rank

sage: E.rank()
 

The elliptic curves in class 250173.bh have rank \(0\).

Modular form 250173.2.a.bh

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

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 LMFDB 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 LMFDB labels.