Properties

Label 4032bj
Number of curves $4$
Conductor $4032$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4032bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.bk4 4032bj1 [0, 0, 0, 36, 432] [2] 1024 \(\Gamma_0(N)\)-optimal
4032.bk3 4032bj2 [0, 0, 0, -684, 6480] [2, 2] 2048  
4032.bk2 4032bj3 [0, 0, 0, -2124, -29808] [2] 4096  
4032.bk1 4032bj4 [0, 0, 0, -10764, 429840] [2] 4096  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 4032bj do not have complex multiplication.

Modular form 4032.2.a.bj

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.