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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 96237.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96237.g1 | 96237e3 | \([0, 0, 1, -4872540, 4139817853]\) | \(727057727488000/37\) | \(651062648637\) | \([]\) | \(829440\) | \(2.1880\) | |
| 96237.g2 | 96237e2 | \([0, 0, 1, -60690, 5572570]\) | \(1404928000/50653\) | \(891304765984053\) | \([]\) | \(276480\) | \(1.6387\) | |
| 96237.g3 | 96237e1 | \([0, 0, 1, -8670, -308291]\) | \(4096000/37\) | \(651062648637\) | \([]\) | \(92160\) | \(1.0894\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96237.g have rank \(0\).
Complex multiplication
The elliptic curves in class 96237.g do not have complex multiplication.Modular form 96237.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
