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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 32487l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32487.f4 | 32487l1 | \([1, 0, 0, -26412, -1654353]\) | \(17319700013617/25857\) | \(3042050193\) | \([2]\) | \(49152\) | \(1.0884\) | \(\Gamma_0(N)\)-optimal |
| 32487.f3 | 32487l2 | \([1, 0, 0, -26657, -1622160]\) | \(17806161424897/668584449\) | \(78658291840401\) | \([2, 2]\) | \(98304\) | \(1.4350\) | |
| 32487.f5 | 32487l3 | \([1, 0, 0, 10828, -5812983]\) | \(1193377118543/124806800313\) | \(-14683395250024137\) | \([2]\) | \(196608\) | \(1.7815\) | |
| 32487.f2 | 32487l4 | \([1, 0, 0, -68062, 4629995]\) | \(296380748763217/92608836489\) | \(10895337004094361\) | \([2, 2]\) | \(196608\) | \(1.7815\) | |
| 32487.f6 | 32487l5 | \([1, 0, 0, 189923, 31408838]\) | \(6439735268725823/7345472585373\) | \(-864187504196548077\) | \([2]\) | \(393216\) | \(2.1281\) | |
| 32487.f1 | 32487l6 | \([1, 0, 0, -988527, 378154692]\) | \(908031902324522977/161726530797\) | \(19026964621736253\) | \([2]\) | \(393216\) | \(2.1281\) |
Rank
sage: E.rank()
The elliptic curves in class 32487l have rank \(1\).
Complex multiplication
The elliptic curves in class 32487l do not have complex multiplication.Modular form 32487.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
