Properties

Label 32487.i
Number of curves $2$
Conductor $32487$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32487.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.i1 32487f1 \([1, 1, 0, -2230, -39017]\) \(10431681625/710073\) \(83539378377\) \([2]\) \(36864\) \(0.84424\) \(\Gamma_0(N)\)-optimal
32487.i2 32487f2 \([1, 1, 0, 1935, -163134]\) \(6804992375/102626433\) \(-12073897216017\) \([2]\) \(73728\) \(1.1908\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32487.2.a.i

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