Properties

Label 250173.g
Number of curves 2
Conductor 250173
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("250173.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.g1 250173g1 [1, -1, 1, -672611, -211460934] [2] 2918400 \(\Gamma_0(N)\)-optimal
250173.g2 250173g2 [1, -1, 1, -363956, -406530894] [2] 5836800  

Rank

sage: E.rank()
 

The elliptic curves in class 250173.g have rank \(1\).

Modular form 250173.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.