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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 162288.fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.fn1 | 162288cl4 | \([0, 0, 0, -872739, -313744158]\) | \(209267191953/55223\) | \(19399731199930368\) | \([2]\) | \(1966080\) | \(2.1098\) | |
| 162288.fn2 | 162288cl2 | \([0, 0, 0, -61299, -3611790]\) | \(72511713/25921\) | \(9105996277518336\) | \([2, 2]\) | \(983040\) | \(1.7632\) | |
| 162288.fn3 | 162288cl1 | \([0, 0, 0, -26019, 1574370]\) | \(5545233/161\) | \(56558983090176\) | \([2]\) | \(491520\) | \(1.4166\) | \(\Gamma_0(N)\)-optimal |
| 162288.fn4 | 162288cl3 | \([0, 0, 0, 185661, -25393662]\) | \(2014698447/1958887\) | \(-688153147258171392\) | \([2]\) | \(1966080\) | \(2.1098\) |
Rank
sage: E.rank()
The elliptic curves in class 162288.fn have rank \(0\).
Complex multiplication
The elliptic curves in class 162288.fn do not have complex multiplication.Modular form 162288.2.a.fn
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.
