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Properties

Label 139230bo
Number of curves $2$
Conductor $139230$
CM no
Rank $1$
Graph

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

Elliptic curves in class 139230bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139230.cn2 139230bo1 \([1, -1, 1, -83948, -10938513]\) \(-89747507348586361/19239456337920\) \(-14025563670343680\) \([2]\) \(1105920\) \(1.8195\) \(\Gamma_0(N)\)-optimal
139230.cn1 139230bo2 \([1, -1, 1, -1405868, -641229969]\) \(421531012285745314681/14601840926400\) \(10644742035345600\) \([2]\) \(2211840\) \(2.1661\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139230bo have rank \(1\).

Complex multiplication

The elliptic curves in class 139230bo do not have complex multiplication.

Modular form 139230.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 2 q^{11} + q^{13} - q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) 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 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.