Properties

Label 166464cw
Number of curves $2$
Conductor $166464$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 166464cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166464.hh1 166464cw1 \([0, 0, 0, -419628, 66423760]\) \(1771561/612\) \(2823009896814870528\) \([2]\) \(3538944\) \(2.2421\) \(\Gamma_0(N)\)-optimal
166464.hh2 166464cw2 \([0, 0, 0, 1245012, 462608080]\) \(46268279/46818\) \(-215960257106337595392\) \([2]\) \(7077888\) \(2.5887\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166464cw have rank \(1\).

Complex multiplication

The elliptic curves in class 166464cw do not have complex multiplication.

Modular form 166464.2.a.cw

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} - 2 q^{7} + 6 q^{13} + 4 q^{19} + O(q^{20})\) 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.