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Properties

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

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

Elliptic curves in class 111090.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.q1 111090x2 \([1, 0, 1, -59751884, 181647832322]\) \(-569508422703721/14527298520\) \(-601815295042806521499480\) \([]\) \(32908032\) \(3.3466\)  
111090.q2 111090x1 \([1, 0, 1, 3212341, 1041249332]\) \(88493315879/62511750\) \(-2589643712359822875750\) \([]\) \(10969344\) \(2.7973\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 111090.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 6 q^{11} + q^{12} - 4 q^{13} + q^{14} - q^{15} + q^{16} - 3 q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.