Properties

Label 36432.bg
Number of curves 2
Conductor 36432
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("36432.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 36432.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
36432.bg1 36432cl2 [0, 0, 0, -178275, -28746974] [2] 163840  
36432.bg2 36432cl1 [0, 0, 0, -3315, -1068302] [2] 81920 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 36432.bg have rank \(1\).

Modular form 36432.2.a.bg

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

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.