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Properties

Label 83490.bo
Number of curves $2$
Conductor $83490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 83490.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83490.bo1 83490bw2 \([1, 1, 1, -29345, 1921745]\) \(1577505447721/838350\) \(1485188164350\) \([2]\) \(403200\) \(1.2853\)  
83490.bo2 83490bw1 \([1, 1, 1, -1515, 40437]\) \(-217081801/285660\) \(-506064115260\) \([2]\) \(201600\) \(0.93872\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 83490.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 83490.bo do not have complex multiplication.

Modular form 83490.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} - q^{12} - 4 q^{13} - 4 q^{14} - q^{15} + q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.