Properties

Label 162450.cf
Number of curves $2$
Conductor $162450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("162450.cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162450.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.cf1 162450eg2 [1, -1, 0, -6003792, 5649327616] [2] 11796480  
162450.cf2 162450eg1 [1, -1, 0, -531792, 7695616] [2] 5898240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 162450.cf have rank \(0\).

Modular form 162450.2.a.cf

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

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.