Properties

Label 193600.bg
Number of curves 2
Conductor 193600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("193600.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bg1 193600gg2 [0, 1, 0, -76633, -8110137] [2] 983040  
193600.bg2 193600gg1 [0, 1, 0, -1008, -320762] [2] 491520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193600.bg have rank \(0\).

Modular form 193600.2.a.bg

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 2q^{7} + q^{9} + 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.