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Properties

Label 32487g
Number of curves $2$
Conductor $32487$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 32487g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.b2 32487g1 \([1, 1, 1, -1618, 23078]\) \(3981876625/232713\) \(27378451737\) \([2]\) \(23040\) \(0.75628\) \(\Gamma_0(N)\)-optimal
32487.b1 32487g2 \([1, 1, 1, -4803, -100500]\) \(104154702625/24649677\) \(2900009849373\) \([2]\) \(46080\) \(1.1029\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32487g have rank \(1\).

Complex multiplication

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

Modular form 32487.2.a.g

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