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Properties

Label 101150g
Number of curves $2$
Conductor $101150$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 101150g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.bg2 101150g1 \([1, 1, 0, -130200, -18056500]\) \(647214625/3332\) \(1256662186062500\) \([2]\) \(663552\) \(1.7431\) \(\Gamma_0(N)\)-optimal
101150.bg1 101150g2 \([1, 1, 0, -202450, 4124250]\) \(2433138625/1387778\) \(523399800495031250\) \([2]\) \(1327104\) \(2.0897\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101150g have rank \(1\).

Complex multiplication

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

Modular form 101150.2.a.g

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