Properties

Label 11088.k
Number of curves $4$
Conductor $11088$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 11088.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11088.k1 11088br3 \([0, 0, 0, -743571, -246792366]\) \(15226621995131793/2324168\) \(6939928461312\) \([2]\) \(73728\) \(1.8696\)  
11088.k2 11088br4 \([0, 0, 0, -86931, 3788370]\) \(24331017010833/12004097336\) \(35844042579738624\) \([2]\) \(73728\) \(1.8696\)  
11088.k3 11088br2 \([0, 0, 0, -46611, -3832110]\) \(3750606459153/45914176\) \(137098994909184\) \([2, 2]\) \(36864\) \(1.5231\)  
11088.k4 11088br1 \([0, 0, 0, -531, -154926]\) \(-5545233/3469312\) \(-10359310123008\) \([2]\) \(18432\) \(1.1765\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11088.k have rank \(0\).

Complex multiplication

The elliptic curves in class 11088.k do not have complex multiplication.

Modular form 11088.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - q^{11} + 2 q^{13} - 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.