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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 990.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 990.j1 | 990k3 | \([1, -1, 1, -37472, -2125731]\) | \(7981893677157049/1917731420550\) | \(1398026205580950\) | \([2]\) | \(5120\) | \(1.6173\) | |
| 990.j2 | 990k2 | \([1, -1, 1, -12722, 527469]\) | \(312341975961049/17862322500\) | \(13021633102500\) | \([2, 2]\) | \(2560\) | \(1.2707\) | |
| 990.j3 | 990k1 | \([1, -1, 1, -12542, 543741]\) | \(299270638153369/1069200\) | \(779446800\) | \([4]\) | \(1280\) | \(0.92414\) | \(\Gamma_0(N)\)-optimal |
| 990.j4 | 990k4 | \([1, -1, 1, 9148, 2137101]\) | \(116149984977671/2779502343750\) | \(-2026257208593750\) | \([2]\) | \(5120\) | \(1.6173\) |
Rank
sage: E.rank()
The elliptic curves in class 990.j have rank \(0\).
Complex multiplication
The elliptic curves in class 990.j do not have complex multiplication.Modular form 990.2.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 LMFDB 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 LMFDB labels.
