Properties

Label 19110.q
Number of curves $2$
Conductor $19110$
CM no
Rank $0$
Graph

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

Elliptic curves in class 19110.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.q1 19110q1 \([1, 1, 0, -4827, 123369]\) \(105756712489/3478020\) \(409185574980\) \([2]\) \(46080\) \(1.0014\) \(\Gamma_0(N)\)-optimal
19110.q2 19110q2 \([1, 1, 0, 1543, 432951]\) \(3449795831/688246650\) \(-80971530125850\) \([2]\) \(92160\) \(1.3480\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19110.q have rank \(0\).

Complex multiplication

The elliptic curves in class 19110.q do not have complex multiplication.

Modular form 19110.2.a.q

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