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Properties

Label 111090.k
Number of curves $2$
Conductor $111090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 111090.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.k1 111090j2 \([1, 1, 0, -104040062, 406861650804]\) \(10236276715651320972447503/45003627643509964800\) \(547559137538585741721600\) \([2]\) \(25804800\) \(3.4076\)  
111090.k2 111090j1 \([1, 1, 0, -9832062, -851731596]\) \(8639211347488146591503/4974033166663680000\) \(60519061538796994560000\) \([2]\) \(12902400\) \(3.0610\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 111090.k have rank \(1\).

Complex multiplication

The elliptic curves in class 111090.k do not have complex multiplication.

Modular form 111090.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} + 4 q^{13} + q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.