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Properties

Label 19110.br
Number of curves $2$
Conductor $19110$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 19110.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.br1 19110br1 \([1, 1, 1, -59046, -5470557]\) \(564174247447/8985600\) \(362601371059200\) \([2]\) \(107520\) \(1.5939\) \(\Gamma_0(N)\)-optimal
19110.br2 19110br2 \([1, 1, 1, -4166, -15173341]\) \(-198155287/2464020000\) \(-99432094720140000\) \([2]\) \(215040\) \(1.9404\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19110.2.a.br

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