Properties

Label 250173o
Number of curves 3
Conductor 250173
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("250173.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.o1 250173o1 [0, 0, 1, -290244, 60186010] [] 1425600 \(\Gamma_0(N)\)-optimal
250173.o2 250173o2 [0, 0, 1, -160284, 114200635] [] 4276800  
250173.o3 250173o3 [0, 0, 1, 1431726, -2955990650] [] 12830400  

Rank

sage: E.rank()
 

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

Modular form 250173.2.a.o

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

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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.