Show commands:
SageMath
E = EllipticCurve("fd1")
E.isogeny_class()
Elliptic curves in class 97344.fd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.fd1 | 97344bo4 | \([0, 0, 0, -22780524, -41849826928]\) | \(11339065490696/351\) | \(40471070641717248\) | \([2]\) | \(4128768\) | \(2.6911\) | |
| 97344.fd2 | 97344bo2 | \([0, 0, 0, -1425684, -652069600]\) | \(22235451328/123201\) | \(1775668224405344256\) | \([2, 2]\) | \(2064384\) | \(2.3445\) | |
| 97344.fd3 | 97344bo3 | \([0, 0, 0, -634764, -1371806800]\) | \(-245314376/6908733\) | \(-796592083440920592384\) | \([2]\) | \(4128768\) | \(2.6911\) | |
| 97344.fd4 | 97344bo1 | \([0, 0, 0, -140439, 2891252]\) | \(1360251712/771147\) | \(173661996484087488\) | \([2]\) | \(1032192\) | \(1.9979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97344.fd have rank \(0\).
Complex multiplication
The elliptic curves in class 97344.fd do not have complex multiplication.Modular form 97344.2.a.fd
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.
