Properties

Label 7350.bg
Number of curves 4
Conductor 7350
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bg1 7350bl4 [1, 0, 1, -1014326, -392004952] [2] 144000  
7350.bg2 7350bl2 [1, 0, 1, -64951, 6365048] [2] 28800  
7350.bg3 7350bl3 [1, 0, 1, -34326, -11764952] [2] 72000  
7350.bg4 7350bl1 [1, 0, 1, -3701, 117548] [2] 14400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7350.bg have rank \(0\).

Modular form 7350.2.a.bg

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

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.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.