Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 33462ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.db4 | 33462ci1 | \([1, -1, 1, -3074, -399]\) | \(912673/528\) | \(1857896705808\) | \([2]\) | \(61440\) | \(1.0437\) | \(\Gamma_0(N)\)-optimal |
| 33462.db2 | 33462ci2 | \([1, -1, 1, -33494, 2360193]\) | \(1180932193/4356\) | \(15327647822916\) | \([2, 2]\) | \(122880\) | \(1.3903\) | |
| 33462.db3 | 33462ci3 | \([1, -1, 1, -18284, 4501761]\) | \(-192100033/2371842\) | \(-8345904239577762\) | \([2]\) | \(245760\) | \(1.7368\) | |
| 33462.db1 | 33462ci4 | \([1, -1, 1, -535424, 150931473]\) | \(4824238966273/66\) | \(232237088226\) | \([2]\) | \(245760\) | \(1.7368\) |
Rank
sage: E.rank()
The elliptic curves in class 33462ci have rank \(1\).
Complex multiplication
The elliptic curves in class 33462ci do not have complex multiplication.Modular form 33462.2.a.ci
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 Cremona 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 Cremona labels.
