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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 386232.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 386232.j1 | 386232j4 | \([0, -1, 0, -71731744, -233814118052]\) | \(22501000029889239268/3620708343\) | \(6568249029461425152\) | \([2]\) | \(31457280\) | \(3.0131\) | |
| 386232.j2 | 386232j2 | \([0, -1, 0, -4496884, -3628851356]\) | \(22174957026242512/278654127129\) | \(126375112732359262464\) | \([2, 2]\) | \(15728640\) | \(2.6665\) | |
| 386232.j3 | 386232j3 | \([0, -1, 0, -772504, -9461230436]\) | \(-28104147578308/21301741002339\) | \(-38643029598048953527296\) | \([2]\) | \(31457280\) | \(3.0131\) | |
| 386232.j4 | 386232j1 | \([0, -1, 0, -527479, 57932008]\) | \(572616640141312/280535480757\) | \(7951771469205626832\) | \([2]\) | \(7864320\) | \(2.3200\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 386232.j have rank \(0\).
Complex multiplication
The elliptic curves in class 386232.j do not have complex multiplication.Modular form 386232.2.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.
