Properties

Label 222768.eo
Number of curves $2$
Conductor $222768$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eo1")
 
E.isogeny_class()
 

Elliptic curves in class 222768.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222768.eo1 222768di2 \([0, 0, 0, -79299, -3285630]\) \(684030715731/338005577\) \(27250539610484736\) \([2]\) \(1474560\) \(1.8467\)  
222768.eo2 222768di1 \([0, 0, 0, -42579, 3346002]\) \(105890949891/1288651\) \(103893064224768\) \([2]\) \(737280\) \(1.5002\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 222768.eo have rank \(1\).

Complex multiplication

The elliptic curves in class 222768.eo do not have complex multiplication.

Modular form 222768.2.a.eo

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - q^{7} - q^{13} + q^{17} + 8 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.