Properties

Label 101150.g
Number of curves $2$
Conductor $101150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 101150.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.g1 101150v2 \([1, 0, 1, -859076, -306546702]\) \(-24843904907425/5488\) \(-15488593750000\) \([]\) \(1244160\) \(1.9140\)  
101150.g2 101150v1 \([1, 0, 1, -9076, -546702]\) \(-29291425/28672\) \(-80920000000000\) \([]\) \(414720\) \(1.3647\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101150.2.a.g

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