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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5082n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5082.n4 | 5082n1 | \([1, 0, 1, -11740, -1791286]\) | \(-100999381393/723148272\) | \(-1281101275892592\) | \([2]\) | \(23040\) | \(1.5820\) | \(\Gamma_0(N)\)-optimal |
| 5082.n3 | 5082n2 | \([1, 0, 1, -304560, -64571894]\) | \(1763535241378513/4612311396\) | \(8170990989009156\) | \([2, 2]\) | \(46080\) | \(1.9286\) | |
| 5082.n1 | 5082n3 | \([1, 0, 1, -4869890, -4136846254]\) | \(7209828390823479793/49509306\) | \(87708755646666\) | \([2]\) | \(92160\) | \(2.2752\) | |
| 5082.n2 | 5082n4 | \([1, 0, 1, -424350, -9085166]\) | \(4770223741048753/2740574865798\) | \(4855095549827970678\) | \([2]\) | \(92160\) | \(2.2752\) |
Rank
sage: E.rank()
The elliptic curves in class 5082n have rank \(0\).
Complex multiplication
The elliptic curves in class 5082n do not have complex multiplication.Modular form 5082.2.a.n
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 Cremona 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 Cremona labels.
