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Properties

Label 11550.bn
Number of curves $2$
Conductor $11550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.bn1 11550bj1 \([1, 1, 1, -2144253, 1211172651]\) \(-43612581618346739773945/147358175518034712\) \(-3683954387950867800\) \([]\) \(311040\) \(2.4268\) \(\Gamma_0(N)\)-optimal
11550.bn2 11550bj2 \([1, 1, 1, 4580772, 6301786941]\) \(425206334414152986757655/931885180314516223488\) \(-23297129507862905587200\) \([]\) \(933120\) \(2.9761\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11550.bn have rank \(0\).

Complex multiplication

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

Modular form 11550.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{11} - q^{12} + q^{13} - q^{14} + q^{16} + 6 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.