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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 105800.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 105800.o1 | 105800v4 | \([0, 0, 0, -1415075, 647892750]\) | \(132304644/5\) | \(11842871120000000\) | \([2]\) | \(1182720\) | \(2.1703\) | |
| 105800.o2 | 105800v2 | \([0, 0, 0, -92575, 9125250]\) | \(148176/25\) | \(14803588900000000\) | \([2, 2]\) | \(591360\) | \(1.8237\) | |
| 105800.o3 | 105800v1 | \([0, 0, 0, -26450, -1520875]\) | \(55296/5\) | \(185044861250000\) | \([2]\) | \(295680\) | \(1.4771\) | \(\Gamma_0(N)\)-optimal |
| 105800.o4 | 105800v3 | \([0, 0, 0, 171925, 51709750]\) | \(237276/625\) | \(-1480358890000000000\) | \([2]\) | \(1182720\) | \(2.1703\) |
Rank
sage: E.rank()
The elliptic curves in class 105800.o have rank \(1\).
Complex multiplication
The elliptic curves in class 105800.o do not have complex multiplication.Modular form 105800.2.a.o
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.
