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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 91200.ff
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.ff1 | 91200ed4 | \([0, 1, 0, -4864033, 4127360063]\) | \(3107086841064961/570\) | \(2334720000000\) | \([2]\) | \(1769472\) | \(2.2090\) | |
| 91200.ff2 | 91200ed3 | \([0, 1, 0, -352033, 42656063]\) | \(1177918188481/488703750\) | \(2001730560000000000\) | \([2]\) | \(1769472\) | \(2.2090\) | |
| 91200.ff3 | 91200ed2 | \([0, 1, 0, -304033, 64400063]\) | \(758800078561/324900\) | \(1330790400000000\) | \([2, 2]\) | \(884736\) | \(1.8624\) | |
| 91200.ff4 | 91200ed1 | \([0, 1, 0, -16033, 1328063]\) | \(-111284641/123120\) | \(-504299520000000\) | \([2]\) | \(442368\) | \(1.5158\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.ff have rank \(1\).
Complex multiplication
The elliptic curves in class 91200.ff do not have complex multiplication.Modular form 91200.2.a.ff
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.
