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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 283920.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.j1 | 283920j1 | \([0, -1, 0, -49451597056, 4232727271161856]\) | \(307903452713493241418533/1106380800000\) | \(48056788991587280486400000\) | \([2]\) | \(402554880\) | \(4.5692\) | \(\Gamma_0(N)\)-optimal |
| 283920.j2 | 283920j2 | \([0, -1, 0, -49429099776, 4236770860277760]\) | \(-307483415359033331264293/583686101250000000\) | \(-25353006672832264258560000000000\) | \([2]\) | \(805109760\) | \(4.9157\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.j have rank \(1\).
Complex multiplication
The elliptic curves in class 283920.j do not have complex multiplication.Modular form 283920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
