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SageMath
E = EllipticCurve("gd1")
E.isogeny_class()
Elliptic curves in class 162240.gd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.gd1 | 162240gq4 | \([0, 1, 0, -335521, -41756545]\) | \(26410345352/10546875\) | \(1668145190400000000\) | \([2]\) | \(2949120\) | \(2.1947\) | |
| 162240.gd2 | 162240gq2 | \([0, 1, 0, -153001, 22526999]\) | \(20034997696/455625\) | \(9007984028160000\) | \([2, 2]\) | \(1474560\) | \(1.8481\) | |
| 162240.gd3 | 162240gq1 | \([0, 1, 0, -152156, 22793850]\) | \(1261112198464/675\) | \(208518148800\) | \([2]\) | \(737280\) | \(1.5015\) | \(\Gamma_0(N)\)-optimal |
| 162240.gd4 | 162240gq3 | \([0, 1, 0, 15999, 69745599]\) | \(2863288/13286025\) | \(-2101382514089164800\) | \([2]\) | \(2949120\) | \(2.1947\) |
Rank
sage: E.rank()
The elliptic curves in class 162240.gd have rank \(0\).
Complex multiplication
The elliptic curves in class 162240.gd do not have complex multiplication.Modular form 162240.2.a.gd
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.
