Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8016.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8016.g1 | 8016j2 | \([0, 1, 0, -200, 564]\) | \(217081801/83667\) | \(342700032\) | \([2]\) | \(5888\) | \(0.33673\) | |
8016.g2 | 8016j1 | \([0, 1, 0, 40, 84]\) | \(1685159/1503\) | \(-6156288\) | \([2]\) | \(2944\) | \(-0.0098414\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8016.g have rank \(1\).
Complex multiplication
The elliptic curves in class 8016.g do not have complex multiplication.Modular form 8016.2.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 LMFDB 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 LMFDB labels.