Properties

Label 32487.c
Number of curves $2$
Conductor $32487$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 32487.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.c1 32487b1 \([1, 1, 1, -22296, -1290024]\) \(10418796526321/6390657\) \(751854405393\) \([2]\) \(107520\) \(1.2216\) \(\Gamma_0(N)\)-optimal
32487.c2 32487b2 \([1, 1, 1, -18131, -1781494]\) \(-5602762882081/8312741073\) \(-977985674497377\) \([2]\) \(215040\) \(1.5682\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32487.2.a.c

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