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)
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.