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Properties

Label 11154.m
Number of curves $2$
Conductor $11154$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 11154.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11154.m1 11154r2 \([1, 0, 1, -10313, -400528]\) \(25128011089/245388\) \(1184441006892\) \([2]\) \(53760\) \(1.1361\)  
11154.m2 11154r1 \([1, 0, 1, -173, -15208]\) \(-117649/20592\) \(-99393650928\) \([2]\) \(26880\) \(0.78953\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11154.m have rank \(0\).

Complex multiplication

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

Modular form 11154.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} + 4 q^{10} - q^{11} + q^{12} - 4 q^{14} - 4 q^{15} + q^{16} + 4 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.