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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 355488.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355488.x1 | 355488x4 | \([0, -1, 0, -118672, -15695528]\) | \(2438569736/21\) | \(1591681878528\) | \([2]\) | \(1576960\) | \(1.5091\) | |
| 355488.x2 | 355488x2 | \([0, -1, 0, -26097, 1364193]\) | \(3241792/567\) | \(343803285762048\) | \([2]\) | \(1576960\) | \(1.5091\) | |
| 355488.x3 | 355488x1 | \([0, -1, 0, -7582, -231800]\) | \(5088448/441\) | \(4178164931136\) | \([2, 2]\) | \(788480\) | \(1.1625\) | \(\Gamma_0(N)\)-optimal |
| 355488.x4 | 355488x3 | \([0, -1, 0, 8288, -1088780]\) | \(830584/7203\) | \(-545946884335104\) | \([2]\) | \(1576960\) | \(1.5091\) |
Rank
sage: E.rank()
The elliptic curves in class 355488.x have rank \(1\).
Complex multiplication
The elliptic curves in class 355488.x do not have complex multiplication.Modular form 355488.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
