Show commands:
SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 243360.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.cy1 | 243360cy2 | \([0, 0, 0, -730587, 240356194]\) | \(23937672968/45\) | \(81071856253440\) | \([2]\) | \(2359296\) | \(1.9241\) | |
| 243360.cy2 | 243360cy4 | \([0, 0, 0, -122187, -11551826]\) | \(111980168/32805\) | \(59101383208757760\) | \([2]\) | \(2359296\) | \(1.9241\) | |
| 243360.cy3 | 243360cy1 | \([0, 0, 0, -46137, 3673384]\) | \(48228544/2025\) | \(456029191425600\) | \([2, 2]\) | \(1179648\) | \(1.5775\) | \(\Gamma_0(N)\)-optimal |
| 243360.cy4 | 243360cy3 | \([0, 0, 0, 22308, 13638976]\) | \(85184/5625\) | \(-81071856253440000\) | \([2]\) | \(2359296\) | \(1.9241\) |
Rank
sage: E.rank()
The elliptic curves in class 243360.cy have rank \(2\).
Complex multiplication
The elliptic curves in class 243360.cy do not have complex multiplication.Modular form 243360.2.a.cy
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.
