Properties

Label 162450v
Number of curves $2$
Conductor $162450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("162450.dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162450v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.dd2 162450v1 [1, -1, 1, -50855, 4557647] [2] 737280 \(\Gamma_0(N)\)-optimal
162450.dd1 162450v2 [1, -1, 1, -820355, 286194647] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 162450v have rank \(1\).

Modular form 162450.2.a.dd

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

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 Cremona 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 Cremona labels.