Properties

Label 162240do
Number of curves $2$
Conductor $162240$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 162240do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.q2 162240do1 \([0, -1, 0, -2721, -57279]\) \(-3869893/300\) \(-172779110400\) \([2]\) \(184320\) \(0.90382\) \(\Gamma_0(N)\)-optimal
162240.q1 162240do2 \([0, -1, 0, -44321, -3576639]\) \(16718302693/90\) \(51833733120\) \([2]\) \(368640\) \(1.2504\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162240do have rank \(1\).

Complex multiplication

The elliptic curves in class 162240do do not have complex multiplication.

Modular form 162240.2.a.do

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 4 q^{11} + q^{15} - 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.