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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2550k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2550.n3 | 2550k1 | \([1, 0, 1, -2526, 42448]\) | \(114013572049/15667200\) | \(244800000000\) | \([2]\) | \(4608\) | \(0.91210\) | \(\Gamma_0(N)\)-optimal |
| 2550.n2 | 2550k2 | \([1, 0, 1, -10526, -373552]\) | \(8253429989329/936360000\) | \(14630625000000\) | \([2, 2]\) | \(9216\) | \(1.2587\) | |
| 2550.n1 | 2550k3 | \([1, 0, 1, -163526, -25465552]\) | \(30949975477232209/478125000\) | \(7470703125000\) | \([2]\) | \(18432\) | \(1.6053\) | |
| 2550.n4 | 2550k4 | \([1, 0, 1, 14474, -1873552]\) | \(21464092074671/109596256200\) | \(-1712441503125000\) | \([2]\) | \(18432\) | \(1.6053\) |
Rank
sage: E.rank()
The elliptic curves in class 2550k have rank \(0\).
Complex multiplication
The elliptic curves in class 2550k do not have complex multiplication.Modular form 2550.2.a.k
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.
