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Properties

Label 266910v
Number of curves $2$
Conductor $266910$
CM no
Rank $0$
Graph

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

Elliptic curves in class 266910v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266910.v1 266910v1 \([1, 0, 1, -16199, 1098146]\) \(-470056203380406889/250217962134840\) \(-250217962134840\) \([3]\) \(1179360\) \(1.4668\) \(\Gamma_0(N)\)-optimal
266910.v2 266910v2 \([1, 0, 1, 128386, -14268688]\) \(234035413953867370151/223522342029504000\) \(-223522342029504000\) \([]\) \(3538080\) \(2.0161\)  

Rank

sage: E.rank()
 

The elliptic curves in class 266910v have rank \(0\).

Complex multiplication

The elliptic curves in class 266910v do not have complex multiplication.

Modular form 266910.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + 2 q^{13} - q^{14} - q^{15} + q^{16} - q^{18} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.