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SageMath
E = EllipticCurve("hl1")
E.isogeny_class()
Elliptic curves in class 91200hl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.hh4 | 91200hl1 | \([0, 1, 0, 1967, -57937]\) | \(3286064/7695\) | \(-1969920000000\) | \([2]\) | \(147456\) | \(1.0431\) | \(\Gamma_0(N)\)-optimal |
| 91200.hh3 | 91200hl2 | \([0, 1, 0, -16033, -651937]\) | \(445138564/81225\) | \(83174400000000\) | \([2, 2]\) | \(294912\) | \(1.3897\) | |
| 91200.hh2 | 91200hl3 | \([0, 1, 0, -76033, 7448063]\) | \(23735908082/1954815\) | \(4003461120000000\) | \([2]\) | \(589824\) | \(1.7362\) | |
| 91200.hh1 | 91200hl4 | \([0, 1, 0, -244033, -46479937]\) | \(784767874322/35625\) | \(72960000000000\) | \([2]\) | \(589824\) | \(1.7362\) |
Rank
sage: E.rank()
The elliptic curves in class 91200hl have rank \(1\).
Complex multiplication
The elliptic curves in class 91200hl do not have complex multiplication.Modular form 91200.2.a.hl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
