Properties

Label 32490bt
Number of curves $2$
Conductor $32490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 32490bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.bq2 32490bt1 \([1, -1, 1, -4746857, 5505632169]\) \(-50284268371/26542080\) \(-6243741160620743393280\) \([2]\) \(1556480\) \(2.8863\) \(\Gamma_0(N)\)-optimal
32490.bq1 32490bt2 \([1, -1, 1, -83762537, 295050689961]\) \(276288773643091/41990400\) \(9877793633013285446400\) \([2]\) \(3112960\) \(3.2329\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32490bt have rank \(0\).

Complex multiplication

The elliptic curves in class 32490bt do not have complex multiplication.

Modular form 32490.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - 2 q^{7} + q^{8} + q^{10} + 2 q^{13} - 2 q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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.