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Properties

Label 11271d
Number of curves $2$
Conductor $11271$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 11271d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11271.h2 11271d1 \([1, 0, 1, -75869, -8042461]\) \(2000852317801/2094417\) \(50554134852273\) \([2]\) \(82944\) \(1.5468\) \(\Gamma_0(N)\)-optimal
11271.h1 11271d2 \([1, 0, 1, -94654, -3759481]\) \(3885442650361/1996623837\) \(48193645632632253\) \([2]\) \(165888\) \(1.8934\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11271d have rank \(0\).

Complex multiplication

The elliptic curves in class 11271d do not have complex multiplication.

Modular form 11271.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + 4 q^{10} - 6 q^{11} - q^{12} - q^{13} - 2 q^{14} + 4 q^{15} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.