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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 72600n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72600.ce4 | 72600n1 | \([0, -1, 0, 2017, -955788]\) | \(2048/891\) | \(-394615212750000\) | \([2]\) | \(368640\) | \(1.4798\) | \(\Gamma_0(N)\)-optimal |
| 72600.ce3 | 72600n2 | \([0, -1, 0, -134108, -18379788]\) | \(37642192/1089\) | \(7716919716000000\) | \([2, 2]\) | \(737280\) | \(1.8264\) | |
| 72600.ce2 | 72600n3 | \([0, -1, 0, -315608, 42241212]\) | \(122657188/43923\) | \(1244996380848000000\) | \([2]\) | \(1474560\) | \(2.1730\) | |
| 72600.ce1 | 72600n4 | \([0, -1, 0, -2130608, -1196314788]\) | \(37736227588/33\) | \(935384208000000\) | \([2]\) | \(1474560\) | \(2.1730\) |
Rank
sage: E.rank()
The elliptic curves in class 72600n have rank \(0\).
Complex multiplication
The elliptic curves in class 72600n do not have complex multiplication.Modular form 72600.2.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.
