Properties

Label 250173.h
Number of curves 4
Conductor 250173
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("250173.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.h1 250173h4 [1, -1, 1, -97785221, -372159762078] [2] 19906560  
250173.h2 250173h3 [1, -1, 1, -8275271, -1338681990] [2] 19906560  
250173.h3 250173h2 [1, -1, 1, -6114686, -5807636004] [2, 2] 9953280  
250173.h4 250173h1 [1, -1, 1, -250241, -154311024] [2] 4976640 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 250173.2.a.h

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.