Show commands:
SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 91200.ef
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.ef1 | 91200fm4 | \([0, -1, 0, -4864033, -4127360063]\) | \(3107086841064961/570\) | \(2334720000000\) | \([2]\) | \(1769472\) | \(2.2090\) | |
| 91200.ef2 | 91200fm3 | \([0, -1, 0, -352033, -42656063]\) | \(1177918188481/488703750\) | \(2001730560000000000\) | \([2]\) | \(1769472\) | \(2.2090\) | |
| 91200.ef3 | 91200fm2 | \([0, -1, 0, -304033, -64400063]\) | \(758800078561/324900\) | \(1330790400000000\) | \([2, 2]\) | \(884736\) | \(1.8624\) | |
| 91200.ef4 | 91200fm1 | \([0, -1, 0, -16033, -1328063]\) | \(-111284641/123120\) | \(-504299520000000\) | \([2]\) | \(442368\) | \(1.5158\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.ef have rank \(0\).
Complex multiplication
The elliptic curves in class 91200.ef do not have complex multiplication.Modular form 91200.2.a.ef
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.
