Show commands:
SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 101430dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.cz3 | 101430dy1 | \([1, -1, 1, -155903, -23653353]\) | \(4886171981209/270480\) | \(23198020408080\) | \([2]\) | \(589824\) | \(1.6301\) | \(\Gamma_0(N)\)-optimal |
| 101430.cz2 | 101430dy2 | \([1, -1, 1, -164723, -20820369]\) | \(5763259856089/1143116100\) | \(98040633749648100\) | \([2, 2]\) | \(1179648\) | \(1.9767\) | |
| 101430.cz4 | 101430dy3 | \([1, -1, 1, 342427, -124076109]\) | \(51774168853511/107398242630\) | \(-9211130672591938230\) | \([2]\) | \(2359296\) | \(2.3233\) | |
| 101430.cz1 | 101430dy4 | \([1, -1, 1, -812993, 263640507]\) | \(692895692874169/51420783750\) | \(4410161161017333750\) | \([2]\) | \(2359296\) | \(2.3233\) |
Rank
sage: E.rank()
The elliptic curves in class 101430dy have rank \(0\).
Complex multiplication
The elliptic curves in class 101430dy do not have complex multiplication.Modular form 101430.2.a.dy
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.
