Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 177600.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177600.j1 | 177600dg2 | \([0, -1, 0, -5833, -157463]\) | \(343000000/26973\) | \(1726272000000\) | \([2]\) | \(331776\) | \(1.0920\) | |
| 177600.j2 | 177600dg1 | \([0, -1, 0, -1208, 13662]\) | \(195112000/36963\) | \(36963000000\) | \([2]\) | \(165888\) | \(0.74538\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177600.j have rank \(0\).
Complex multiplication
The elliptic curves in class 177600.j do not have complex multiplication.Modular form 177600.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
