Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("250173.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.x1 250173x2 [0, 0, 1, -9010560, -10444578260] [] 8709120  
250173.x2 250173x1 [0, 0, 1, 249090, -75066611] [] 2903040 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 250173.2.a.x

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.