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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 34650.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34650.cl1 | 34650dx4 | \([1, -1, 1, -1497325055, -22299890030553]\) | \(260744057755293612689909/8504954620259328\) | \(12109593590173926000000000\) | \([2]\) | \(15360000\) | \(3.9070\) | |
| 34650.cl2 | 34650dx3 | \([1, -1, 1, -97645055, -316515950553]\) | \(72313087342699809269/11447096545640448\) | \(16298698011273216000000000\) | \([2]\) | \(7680000\) | \(3.5605\) | |
| 34650.cl3 | 34650dx2 | \([1, -1, 1, -26494430, 52016015697]\) | \(1444540994277943589/15251205665388\) | \(21715095566538773437500\) | \([2]\) | \(3072000\) | \(3.1023\) | |
| 34650.cl4 | 34650dx1 | \([1, -1, 1, -26426930, 52296545697]\) | \(1433528304665250149/162339408\) | \(231143414906250000\) | \([2]\) | \(1536000\) | \(2.7557\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 34650.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 34650.cl do not have complex multiplication.Modular form 34650.2.a.cl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
