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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 80736.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80736.n1 | 80736c4 | \([0, 1, 0, -27192, -1734360]\) | \(7301384/3\) | \(913648621056\) | \([2]\) | \(200704\) | \(1.2574\) | |
| 80736.n2 | 80736c3 | \([0, 1, 0, -14577, 659967]\) | \(140608/3\) | \(7309188968448\) | \([2]\) | \(200704\) | \(1.2574\) | |
| 80736.n3 | 80736c1 | \([0, 1, 0, -1962, -18720]\) | \(21952/9\) | \(342618232896\) | \([2, 2]\) | \(100352\) | \(0.91085\) | \(\Gamma_0(N)\)-optimal |
| 80736.n4 | 80736c2 | \([0, 1, 0, 6448, -129732]\) | \(97336/81\) | \(-24668512768512\) | \([2]\) | \(200704\) | \(1.2574\) |
Rank
sage: E.rank()
The elliptic curves in class 80736.n have rank \(0\).
Complex multiplication
The elliptic curves in class 80736.n do not have complex multiplication.Modular form 80736.2.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 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.
