Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1360f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1360.i2 | 1360f1 | \([0, -1, 0, -40856, -3164944]\) | \(1841373668746009/31443200\) | \(128791347200\) | \([2]\) | \(3840\) | \(1.2613\) | \(\Gamma_0(N)\)-optimal |
| 1360.i3 | 1360f2 | \([0, -1, 0, -39576, -3373840]\) | \(-1673672305534489/241375690000\) | \(-988674826240000\) | \([2]\) | \(7680\) | \(1.6079\) | |
| 1360.i1 | 1360f3 | \([0, -1, 0, -66696, 1326320]\) | \(8010684753304969/4456448000000\) | \(18253611008000000\) | \([2]\) | \(11520\) | \(1.8106\) | |
| 1360.i4 | 1360f4 | \([0, -1, 0, 260984, 10239216]\) | \(479958568556831351/289000000000000\) | \(-1183744000000000000\) | \([2]\) | \(23040\) | \(2.1572\) |
Rank
sage: E.rank()
The elliptic curves in class 1360f have rank \(1\).
Complex multiplication
The elliptic curves in class 1360f do not have complex multiplication.Modular form 1360.2.a.f
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
