Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 18864.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18864.g1 | 18864bh3 | \([0, 0, 0, -804891, 277941706]\) | \(19312898130234073/84888\) | \(253474209792\) | \([2]\) | \(110592\) | \(1.8165\) | |
| 18864.g2 | 18864bh2 | \([0, 0, 0, -50331, 4338250]\) | \(4722184089433/9884736\) | \(29515663540224\) | \([2, 2]\) | \(55296\) | \(1.4700\) | |
| 18864.g3 | 18864bh4 | \([0, 0, 0, -33051, 7362250]\) | \(-1337180541913/7067998104\) | \(-21104929250574336\) | \([4]\) | \(110592\) | \(1.8165\) | |
| 18864.g4 | 18864bh1 | \([0, 0, 0, -4251, 15946]\) | \(2845178713/1609728\) | \(4806622052352\) | \([2]\) | \(27648\) | \(1.1234\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18864.g have rank \(0\).
Complex multiplication
The elliptic curves in class 18864.g do not have complex multiplication.Modular form 18864.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
