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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 14994cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14994.bl1 | 14994cs1 | \([1, -1, 1, -1112, 9335]\) | \(1771561/612\) | \(52488866052\) | \([2]\) | \(23040\) | \(0.75873\) | \(\Gamma_0(N)\)-optimal |
| 14994.bl2 | 14994cs2 | \([1, -1, 1, 3298, 62255]\) | \(46268279/46818\) | \(-4015398252978\) | \([2]\) | \(46080\) | \(1.1053\) |
Rank
sage: E.rank()
The elliptic curves in class 14994cs have rank \(0\).
Complex multiplication
The elliptic curves in class 14994cs do not have complex multiplication.Modular form 14994.2.a.cs
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
