Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("250173.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.n2 250173n1 [0, 0, 1, -766764, -258428258] [] 1866240 \(\Gamma_0(N)\)-optimal
250173.n1 250173n2 [0, 0, 1, -994194, -92735395] [] 5598720  

Rank

sage: E.rank()
 

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

Modular form 250173.2.a.n

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.