Show commands:
SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 41280.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.de1 | 41280bk4 | \([0, 1, 0, -44065, 3545663]\) | \(36097320816649/80625\) | \(21135360000\) | \([2]\) | \(90112\) | \(1.2264\) | |
| 41280.de2 | 41280bk3 | \([0, 1, 0, -7585, -185665]\) | \(184122897769/51282015\) | \(13443272540160\) | \([2]\) | \(90112\) | \(1.2264\) | |
| 41280.de3 | 41280bk2 | \([0, 1, 0, -2785, 53375]\) | \(9116230969/416025\) | \(109058457600\) | \([2, 2]\) | \(45056\) | \(0.87979\) | |
| 41280.de4 | 41280bk1 | \([0, 1, 0, 95, 3263]\) | \(357911/17415\) | \(-4565237760\) | \([2]\) | \(22528\) | \(0.53322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41280.de have rank \(1\).
Complex multiplication
The elliptic curves in class 41280.de do not have complex multiplication.Modular form 41280.2.a.de
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.
