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SageMath
E = EllipticCurve("ki1")
E.isogeny_class()
Elliptic curves in class 327600ki
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327600.ki4 | 327600ki1 | \([0, 0, 0, -840675, 296289250]\) | \(1408317602329/2153060\) | \(100453167360000000\) | \([2]\) | \(3981312\) | \(2.1620\) | \(\Gamma_0(N)\)-optimal |
| 327600.ki3 | 327600ki2 | \([0, 0, 0, -1092675, 104013250]\) | \(3092354182009/1689383150\) | \(78819860246400000000\) | \([2]\) | \(7962624\) | \(2.5086\) | |
| 327600.ki2 | 327600ki3 | \([0, 0, 0, -3414675, -2139416750]\) | \(94376601570889/12235496000\) | \(570859301376000000000\) | \([2]\) | \(11943936\) | \(2.7113\) | |
| 327600.ki1 | 327600ki4 | \([0, 0, 0, -52806675, -147697640750]\) | \(349046010201856969/7245875000\) | \(338063544000000000000\) | \([2]\) | \(23887872\) | \(3.0579\) |
Rank
sage: E.rank()
The elliptic curves in class 327600ki have rank \(0\).
Complex multiplication
The elliptic curves in class 327600ki do not have complex multiplication.Modular form 327600.2.a.ki
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
