Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162450v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162450.dd2 162450v1 \([1, -1, 1, -50855, 4557647]\) \(-186169411/6480\) \(-506271363750000\) \([2]\) \(737280\) \(1.5945\) \(\Gamma_0(N)\)-optimal
162450.dd1 162450v2 \([1, -1, 1, -820355, 286194647]\) \(781484460931/900\) \(70315467187500\) \([2]\) \(1474560\) \(1.9410\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 162450v do not have complex multiplication.

Modular form 162450.2.a.v

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

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.