↑

Properties

Label 11550.bx
Number of curves $2$
Conductor $11550$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 11550.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.bx1 11550cd2 \([1, 1, 1, -23883, 1410681]\) \(12052620205076933/8781696\) \(1097712000\) \([2]\) \(28672\) \(1.0459\)  
11550.bx2 11550cd1 \([1, 1, 1, -1483, 21881]\) \(-2885728410053/79478784\) \(-9934848000\) \([2]\) \(14336\) \(0.69931\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11550.bx have rank \(1\).

Complex multiplication

The elliptic curves in class 11550.bx do not have complex multiplication.

Modular form 11550.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} + q^{11} - q^{12} - 6 q^{13} + q^{14} + q^{16} - 6 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.