Properties

Label 4032.bb
Number of curves 4
Conductor 4032
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4032.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4032.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.bb1 4032g3 [0, 0, 0, -10764, -429840] [2] 4096  
4032.bb2 4032g4 [0, 0, 0, -2124, 29808] [2] 4096  
4032.bb3 4032g2 [0, 0, 0, -684, -6480] [2, 2] 2048  
4032.bb4 4032g1 [0, 0, 0, 36, -432] [2] 1024 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4032.bb have rank \(0\).

Modular form 4032.2.a.bb

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} - 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.