Properties

Label 151008g
Number of curves $2$
Conductor $151008$
CM no
Rank $0$
Graph

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

Elliptic curves in class 151008g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151008.bq2 151008g1 \([0, 1, 0, -11898, -223236]\) \(1643032000/767637\) \(87034609366848\) \([2]\) \(409600\) \(1.3692\) \(\Gamma_0(N)\)-optimal
151008.bq1 151008g2 \([0, 1, 0, -158913, -24421905]\) \(61162984000/41067\) \(297995041124352\) \([2]\) \(819200\) \(1.7158\)  

Rank

sage: E.rank()
 

The elliptic curves in class 151008g have rank \(0\).

Complex multiplication

The elliptic curves in class 151008g do not have complex multiplication.

Modular form 151008.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} - q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.