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Properties

Label 101150bo
Number of curves $2$
Conductor $101150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 101150bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.cd2 101150bo1 \([1, -1, 1, 13095, 284597]\) \(658503/476\) \(-179523169437500\) \([2]\) \(294912\) \(1.4235\) \(\Gamma_0(N)\)-optimal
101150.cd1 101150bo2 \([1, -1, 1, -59155, 2452097]\) \(60698457/28322\) \(10681628581531250\) \([2]\) \(589824\) \(1.7700\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101150bo have rank \(0\).

Complex multiplication

The elliptic curves in class 101150bo do not have complex multiplication.

Modular form 101150.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{9} + 2 q^{11} - q^{14} + q^{16} - 3 q^{18} - 2 q^{19} + O(q^{20})\) 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.