Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 55488j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55488.bs3 | 55488j1 | \([0, -1, 0, -1252, 17158]\) | \(140608/3\) | \(4634413248\) | \([2]\) | \(36864\) | \(0.64381\) | \(\Gamma_0(N)\)-optimal |
| 55488.bs2 | 55488j2 | \([0, -1, 0, -2697, -28215]\) | \(21952/9\) | \(889807343616\) | \([2, 2]\) | \(73728\) | \(0.99039\) | |
| 55488.bs4 | 55488j3 | \([0, -1, 0, 8863, -215487]\) | \(97336/81\) | \(-64066128740352\) | \([2]\) | \(147456\) | \(1.3370\) | |
| 55488.bs1 | 55488j4 | \([0, -1, 0, -37377, -2767935]\) | \(7301384/3\) | \(2372819582976\) | \([2]\) | \(147456\) | \(1.3370\) |
Rank
sage: E.rank()
The elliptic curves in class 55488j have rank \(1\).
Complex multiplication
The elliptic curves in class 55488j do not have complex multiplication.Modular form 55488.2.a.j
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.
