Properties

Label 890g
Number of curves $2$
Conductor $890$
CM no
Rank $1$
Graph

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

Elliptic curves in class 890g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
890.g2 890g1 \([1, 1, 1, 10, 147]\) \(109902239/8900000\) \(-8900000\) \([5]\) \(200\) \(0.012969\) \(\Gamma_0(N)\)-optimal
890.g1 890g2 \([1, 1, 1, -2040, -38093]\) \(-938917686360961/55840594490\) \(-55840594490\) \([]\) \(1000\) \(0.81769\)  

Rank

sage: E.rank()
 

The elliptic curves in class 890g have rank \(1\).

Complex multiplication

The elliptic curves in class 890g do not have complex multiplication.

Modular form 890.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2 q^{7} + q^{8} - 2 q^{9} + q^{10} - 3 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} - q^{15} + q^{16} - 2 q^{17} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.