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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 13200.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.n1 | 13200bi5 | \([0, -1, 0, -68434008, 217922230512]\) | \(553808571467029327441/12529687500\) | \(801900000000000000\) | \([2]\) | \(884736\) | \(2.9596\) | |
| 13200.n2 | 13200bi3 | \([0, -1, 0, -4730008, -3949257488]\) | \(182864522286982801/463015182960\) | \(29632971709440000000\) | \([2]\) | \(442368\) | \(2.6131\) | |
| 13200.n3 | 13200bi4 | \([0, -1, 0, -4282008, 3397942512]\) | \(135670761487282321/643043610000\) | \(41154791040000000000\) | \([2, 2]\) | \(442368\) | \(2.6131\) | |
| 13200.n4 | 13200bi6 | \([0, -1, 0, -2082008, 6882742512]\) | \(-15595206456730321/310672490129100\) | \(-19883039368262400000000\) | \([2]\) | \(884736\) | \(2.9596\) | |
| 13200.n5 | 13200bi2 | \([0, -1, 0, -410008, -9417488]\) | \(119102750067601/68309049600\) | \(4371779174400000000\) | \([2, 2]\) | \(221184\) | \(2.2665\) | |
| 13200.n6 | 13200bi1 | \([0, -1, 0, 101992, -1225488]\) | \(1833318007919/1070530560\) | \(-68513955840000000\) | \([2]\) | \(110592\) | \(1.9199\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13200.n have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.n do not have complex multiplication.Modular form 13200.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
