Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 179520.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.dj1 | 179520hb1 | \([0, -1, 0, -544225, 154710625]\) | \(68001744211490809/1022422500\) | \(268021923840000\) | \([2]\) | \(1548288\) | \(1.9051\) | \(\Gamma_0(N)\)-optimal |
| 179520.dj2 | 179520hb2 | \([0, -1, 0, -528225, 164217825]\) | \(-62178675647294809/8362782148050\) | \(-2192253163418419200\) | \([2]\) | \(3096576\) | \(2.2517\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.dj have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.dj do not have complex multiplication.Modular form 179520.2.a.dj
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.
