Properties

Label 66240do
Number of curves $2$
Conductor $66240$
CM no
Rank $1$
Graph

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

Elliptic curves in class 66240do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66240.cn2 66240do1 \([0, 0, 0, 132, -8208]\) \(574992/66125\) \(-29251584000\) \([2]\) \(36864\) \(0.68765\) \(\Gamma_0(N)\)-optimal
66240.cn1 66240do2 \([0, 0, 0, -5388, -147312]\) \(9776035692/359375\) \(635904000000\) \([2]\) \(73728\) \(1.0342\)  

Rank

sage: E.rank()
 

The elliptic curves in class 66240do have rank \(1\).

Complex multiplication

The elliptic curves in class 66240do do not have complex multiplication.

Modular form 66240.2.a.do

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{7} + 2 q^{13} + 6 q^{17} + O(q^{20})\) 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.