Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 91200.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.f1 | 91200fn4 | \([0, -1, 0, -1548033, 741707937]\) | \(100162392144121/23457780\) | \(96083066880000000\) | \([2]\) | \(2359296\) | \(2.2491\) | |
| 91200.f2 | 91200fn3 | \([0, -1, 0, -716033, -226548063]\) | \(9912050027641/311647500\) | \(1276508160000000000\) | \([2]\) | \(2359296\) | \(2.2491\) | |
| 91200.f3 | 91200fn2 | \([0, -1, 0, -108033, 8747937]\) | \(34043726521/11696400\) | \(47908454400000000\) | \([2, 2]\) | \(1179648\) | \(1.9026\) | |
| 91200.f4 | 91200fn1 | \([0, -1, 0, 19967, 939937]\) | \(214921799/218880\) | \(-896532480000000\) | \([2]\) | \(589824\) | \(1.5560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.f have rank \(0\).
Complex multiplication
The elliptic curves in class 91200.f do not have complex multiplication.Modular form 91200.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
