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Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 11154p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11154.t2 11154p1 \([1, 0, 1, -342, 2368]\) \(154241737/2376\) \(67860936\) \([3]\) \(7776\) \(0.30419\) \(\Gamma_0(N)\)-optimal
11154.t1 11154p2 \([1, 0, 1, -2877, -58472]\) \(92162208697/2044416\) \(58390565376\) \([]\) \(23328\) \(0.85350\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11154.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.