Properties

Label 19110.bg
Number of curves $4$
Conductor $19110$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 19110.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.bg1 19110bh3 \([1, 0, 1, -23693, 1401446]\) \(12501706118329/2570490\) \(302415578010\) \([2]\) \(49152\) \(1.2000\)  
19110.bg2 19110bh2 \([1, 0, 1, -1643, 16706]\) \(4165509529/1368900\) \(161049716100\) \([2, 2]\) \(24576\) \(0.85341\)  
19110.bg3 19110bh1 \([1, 0, 1, -663, -6422]\) \(273359449/9360\) \(1101194640\) \([2]\) \(12288\) \(0.50684\) \(\Gamma_0(N)\)-optimal
19110.bg4 19110bh4 \([1, 0, 1, 4727, 116078]\) \(99317171591/106616250\) \(-12543295196250\) \([2]\) \(49152\) \(1.2000\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19110.bg have rank \(1\).

Complex multiplication

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

Modular form 19110.2.a.bg

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.