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Properties

Label 101150.ba
Number of curves $2$
Conductor $101150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 101150.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.ba1 101150s2 \([1, 0, 1, -13156, -817172]\) \(-417267265/235298\) \(-141988042764050\) \([]\) \(362880\) \(1.4187\)  
101150.ba2 101150s1 \([1, 0, 1, 1294, 15148]\) \(397535/392\) \(-236548176200\) \([]\) \(120960\) \(0.86944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101150.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} - 2 q^{9} - 3 q^{11} + q^{12} - 2 q^{13} - q^{14} + q^{16} + 2 q^{18} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.