Properties

Label 11466.bj
Number of curves $3$
Conductor $11466$
CM no
Rank $0$
Graph

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

Elliptic curves in class 11466.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11466.bj1 11466cd3 \([1, -1, 1, -202649, -35062023]\) \(-10730978619193/6656\) \(-570859301376\) \([]\) \(68040\) \(1.5766\)  
11466.bj2 11466cd2 \([1, -1, 1, -1994, -67791]\) \(-10218313/17576\) \(-1507425342696\) \([]\) \(22680\) \(1.0273\)  
11466.bj3 11466cd1 \([1, -1, 1, 211, 1887]\) \(12167/26\) \(-2229919146\) \([]\) \(7560\) \(0.47804\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11466.bj have rank \(0\).

Complex multiplication

The elliptic curves in class 11466.bj do not have complex multiplication.

Modular form 11466.2.a.bj

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.