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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 91200dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.jf4 | 91200dy1 | \([0, 1, 0, 19967, -939937]\) | \(214921799/218880\) | \(-896532480000000\) | \([2]\) | \(589824\) | \(1.5560\) | \(\Gamma_0(N)\)-optimal |
| 91200.jf3 | 91200dy2 | \([0, 1, 0, -108033, -8747937]\) | \(34043726521/11696400\) | \(47908454400000000\) | \([2, 2]\) | \(1179648\) | \(1.9026\) | |
| 91200.jf2 | 91200dy3 | \([0, 1, 0, -716033, 226548063]\) | \(9912050027641/311647500\) | \(1276508160000000000\) | \([2]\) | \(2359296\) | \(2.2491\) | |
| 91200.jf1 | 91200dy4 | \([0, 1, 0, -1548033, -741707937]\) | \(100162392144121/23457780\) | \(96083066880000000\) | \([2]\) | \(2359296\) | \(2.2491\) |
Rank
sage: E.rank()
The elliptic curves in class 91200dy have rank \(1\).
Complex multiplication
The elliptic curves in class 91200dy do not have complex multiplication.Modular form 91200.2.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.
