Properties

Label 4032.j
Number of curves $2$
Conductor $4032$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 4032.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.j1 4032d1 \([0, 0, 0, -216, -1080]\) \(55296/7\) \(141087744\) \([2]\) \(1536\) \(0.29296\) \(\Gamma_0(N)\)-optimal
4032.j2 4032d2 \([0, 0, 0, 324, -5616]\) \(11664/49\) \(-15801827328\) \([2]\) \(3072\) \(0.63953\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4032.2.a.j

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

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.