Properties

Label 32487.j
Number of curves $2$
Conductor $32487$
CM no
Rank $0$
Graph

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

Elliptic curves in class 32487.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.j1 32487r2 \([1, 0, 1, -16049, 260579]\) \(3885442650361/1996623837\) \(234900797799213\) \([2]\) \(207360\) \(1.4497\)  
32487.j2 32487r1 \([1, 0, 1, -12864, 559969]\) \(2000852317801/2094417\) \(246406065633\) \([2]\) \(103680\) \(1.1031\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32487.j have rank \(0\).

Complex multiplication

The elliptic curves in class 32487.j do not have complex multiplication.

Modular form 32487.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 3 q^{8} + q^{9} + 4 q^{10} + 6 q^{11} - q^{12} + q^{13} + 4 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.