↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.bj1 11550by2 \([1, 1, 1, -328, -2419]\) \(31226116949/71148\) \(8893500\) \([2]\) \(5120\) \(0.21489\)  
11550.bj2 11550by1 \([1, 1, 1, -28, -19]\) \(19465109/11088\) \(1386000\) \([2]\) \(2560\) \(-0.13168\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11550.2.a.bj

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