Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8624.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8624.o1 | 8624w3 | \([0, 0, 0, -4048331, -3135177094]\) | \(15226621995131793/2324168\) | \(1119994024067072\) | \([2]\) | \(110592\) | \(2.2933\) | |
| 8624.o2 | 8624w4 | \([0, 0, 0, -473291, 48126330]\) | \(24331017010833/12004097336\) | \(5784658114490630144\) | \([4]\) | \(110592\) | \(2.2933\) | |
| 8624.o3 | 8624w2 | \([0, 0, 0, -253771, -48681990]\) | \(3750606459153/45914176\) | \(22125596230549504\) | \([2, 2]\) | \(55296\) | \(1.9467\) | |
| 8624.o4 | 8624w1 | \([0, 0, 0, -2891, -1968134]\) | \(-5545233/3469312\) | \(-1671827814350848\) | \([2]\) | \(27648\) | \(1.6001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8624.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8624.o do not have complex multiplication.Modular form 8624.2.a.o
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.
