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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 61200.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61200.g1 | 61200gd4 | \([0, 0, 0, -23547675, -43980925750]\) | \(30949975477232209/478125000\) | \(22307400000000000000\) | \([2]\) | \(3538944\) | \(2.8477\) | |
| 61200.g2 | 61200gd2 | \([0, 0, 0, -1515675, -643981750]\) | \(8253429989329/936360000\) | \(43686812160000000000\) | \([2, 2]\) | \(1769472\) | \(2.5011\) | |
| 61200.g3 | 61200gd1 | \([0, 0, 0, -363675, 73714250]\) | \(114013572049/15667200\) | \(730968883200000000\) | \([2]\) | \(884736\) | \(2.1546\) | \(\Gamma_0(N)\)-optimal |
| 61200.g4 | 61200gd3 | \([0, 0, 0, 2084325, -3239581750]\) | \(21464092074671/109596256200\) | \(-5113322929267200000000\) | \([2]\) | \(3538944\) | \(2.8477\) |
Rank
sage: E.rank()
The elliptic curves in class 61200.g have rank \(0\).
Complex multiplication
The elliptic curves in class 61200.g do not have complex multiplication.Modular form 61200.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
