Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1584.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1584.g1 | 1584p3 | \([0, 0, 0, -1126128, -459970256]\) | \(-52893159101157376/11\) | \(-32845824\) | \([]\) | \(6000\) | \(1.7392\) | |
| 1584.g2 | 1584p2 | \([0, 0, 0, -1488, -40016]\) | \(-122023936/161051\) | \(-480895709184\) | \([]\) | \(1200\) | \(0.93444\) | |
| 1584.g3 | 1584p1 | \([0, 0, 0, -48, 304]\) | \(-4096/11\) | \(-32845824\) | \([]\) | \(240\) | \(0.12972\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1584.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1584.g do not have complex multiplication.Modular form 1584.2.a.g
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
