Properties

Label 266616.bx
Number of curves $2$
Conductor $266616$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 266616.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266616.bx1 266616bx2 \([0, 0, 0, -4661019, 3873121110]\) \(50668941906/1127\) \(249085480534603776\) \([2]\) \(4325376\) \(2.4530\)  
266616.bx2 266616bx1 \([0, 0, 0, -280899, 65044782]\) \(-22180932/3703\) \(-409211860878277632\) \([2]\) \(2162688\) \(2.1064\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 266616.bx have rank \(1\).

Complex multiplication

The elliptic curves in class 266616.bx do not have complex multiplication.

Modular form 266616.2.a.bx

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} - 4 q^{13} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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.