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Properties

Label 11154.a
Number of curves $2$
Conductor $11154$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 11154.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11154.a1 11154f2 \([1, 1, 0, -6229512, -5987113920]\) \(5538928862777598289/141343488\) \(682238019969792\) \([2]\) \(387072\) \(2.3629\)  
11154.a2 11154f1 \([1, 1, 0, -388872, -93908160]\) \(-1347365318848849/6831931392\) \(-32976427930288128\) \([2]\) \(193536\) \(2.0164\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11154.a have rank \(1\).

Complex multiplication

The elliptic curves in class 11154.a do not have complex multiplication.

Modular form 11154.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 4 q^{5} + q^{6} - q^{8} + q^{9} + 4 q^{10} - q^{11} - q^{12} + 4 q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.