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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 52800.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.fv1 | 52800gu6 | \([0, 1, 0, -273736033, 1743104108063]\) | \(553808571467029327441/12529687500\) | \(51321600000000000000\) | \([2]\) | \(7077888\) | \(3.3062\) | |
| 52800.fv2 | 52800gu4 | \([0, 1, 0, -18920033, -31612979937]\) | \(182864522286982801/463015182960\) | \(1896510189404160000000\) | \([2]\) | \(3538944\) | \(2.9596\) | |
| 52800.fv3 | 52800gu3 | \([0, 1, 0, -17128033, 27166412063]\) | \(135670761487282321/643043610000\) | \(2633906626560000000000\) | \([2, 2]\) | \(3538944\) | \(2.9596\) | |
| 52800.fv4 | 52800gu5 | \([0, 1, 0, -8328033, 55053612063]\) | \(-15595206456730321/310672490129100\) | \(-1272514519568793600000000\) | \([2]\) | \(7077888\) | \(3.3062\) | |
| 52800.fv5 | 52800gu2 | \([0, 1, 0, -1640033, -76979937]\) | \(119102750067601/68309049600\) | \(279793867161600000000\) | \([2, 2]\) | \(1769472\) | \(2.6131\) | |
| 52800.fv6 | 52800gu1 | \([0, 1, 0, 407967, -9395937]\) | \(1833318007919/1070530560\) | \(-4384893173760000000\) | \([2]\) | \(884736\) | \(2.2665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52800.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 52800.fv do not have complex multiplication.Modular form 52800.2.a.fv
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.
