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Properties

Label 11270.q
Number of curves $2$
Conductor $11270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 11270.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11270.q1 11270n2 \([1, 1, 1, -1230881, 381655903]\) \(1753007192038126081/478174101507200\) \(56256704868220572800\) \([2]\) \(430080\) \(2.4975\)  
11270.q2 11270n1 \([1, 1, 1, -446881, -110382497]\) \(83890194895342081/3958384640000\) \(465699994511360000\) \([2]\) \(215040\) \(2.1509\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11270.q have rank \(0\).

Complex multiplication

The elliptic curves in class 11270.q do not have complex multiplication.

Modular form 11270.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{8} + q^{9} - q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.