Properties

Label 349140.bg
Number of curves $4$
Conductor $349140$
CM no
Rank $1$
Graph

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

Elliptic curves in class 349140.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349140.bg1 349140bg4 \([0, 1, 0, -132248060, 585328098900]\) \(6749703004355978704/5671875\) \(214948110828000000\) \([2]\) \(21897216\) \(3.0613\)  
349140.bg2 349140bg3 \([0, 1, 0, -8263685, 9147911400]\) \(-26348629355659264/24169921875\) \(-57248253949218750000\) \([2]\) \(10948608\) \(2.7147\)  
349140.bg3 349140bg2 \([0, 1, 0, -1669700, 764114148]\) \(13584145739344/1195803675\) \(45317596185111571200\) \([2]\) \(7299072\) \(2.5120\)  
349140.bg4 349140bg1 \([0, 1, 0, 115675, 55677348]\) \(72268906496/606436875\) \(-1436390750608110000\) \([2]\) \(3649536\) \(2.1654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 349140.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 349140.bg do not have complex multiplication.

Modular form 349140.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2q^{7} + q^{9} - q^{11} + 2q^{13} + q^{15} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.