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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 92736.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.eb1 | 92736dx4 | \([0, 0, 0, -71244, 7317648]\) | \(209267191953/55223\) | \(10553279643648\) | \([2]\) | \(327680\) | \(1.4834\) | |
| 92736.eb2 | 92736dx2 | \([0, 0, 0, -5004, 84240]\) | \(72511713/25921\) | \(4953580240896\) | \([2, 2]\) | \(163840\) | \(1.1368\) | |
| 92736.eb3 | 92736dx1 | \([0, 0, 0, -2124, -36720]\) | \(5545233/161\) | \(30767579136\) | \([2]\) | \(81920\) | \(0.79025\) | \(\Gamma_0(N)\)-optimal |
| 92736.eb4 | 92736dx3 | \([0, 0, 0, 15156, 592272]\) | \(2014698447/1958887\) | \(-374349135347712\) | \([2]\) | \(327680\) | \(1.4834\) |
Rank
sage: E.rank()
The elliptic curves in class 92736.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 92736.eb do not have complex multiplication.Modular form 92736.2.a.eb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
