Properties

Label 2093g
Number of curves $2$
Conductor $2093$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2093g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2093.g1 2093g1 \([0, 1, 1, -43687, 3500082]\) \(-9221261135586623488/121324931\) \(-121324931\) \([3]\) \(3456\) \(1.1095\) \(\Gamma_0(N)\)-optimal
2093.g2 2093g2 \([0, 1, 1, -41217, 3915835]\) \(-7743965038771437568/2189290237869371\) \(-2189290237869371\) \([]\) \(10368\) \(1.6589\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2093g have rank \(1\).

Complex multiplication

The elliptic curves in class 2093g do not have complex multiplication.

Modular form 2093.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - 3 q^{5} + q^{7} - 2 q^{9} + 3 q^{11} - 2 q^{12} + q^{13} - 3 q^{15} + 4 q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.