Properties

Label 11271h
Number of curves $6$
Conductor $11271$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11271.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11271h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11271.e4 11271h1 [1, 0, 0, -155777, 23651808] [4] 36864 \(\Gamma_0(N)\)-optimal
11271.e3 11271h2 [1, 0, 0, -157222, 23190275] [2, 2] 73728  
11271.e2 11271h3 [1, 0, 0, -401427, -66432960] [2, 2] 147456  
11271.e5 11271h4 [1, 0, 0, 63863, 83281178] [2] 147456  
11271.e1 11271h5 [1, 0, 0, -5830292, -5418208077] [2] 294912  
11271.e6 11271h6 [1, 0, 0, 1120158, -449568063] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 11271h have rank \(1\).

Modular form 11271.2.a.e

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.