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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 39600.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.cn1 | 39600cx6 | \([0, 0, 0, -13986075, -20131469750]\) | \(6484907238722641/283593750\) | \(13231350000000000000\) | \([2]\) | \(1179648\) | \(2.7473\) | |
| 39600.cn2 | 39600cx4 | \([0, 0, 0, -4230075, 3348630250]\) | \(179415687049201/1443420\) | \(67344203520000000\) | \([2]\) | \(589824\) | \(2.4007\) | |
| 39600.cn3 | 39600cx3 | \([0, 0, 0, -918075, -281177750]\) | \(1834216913521/329422500\) | \(15369536160000000000\) | \([2, 2]\) | \(589824\) | \(2.4007\) | |
| 39600.cn4 | 39600cx2 | \([0, 0, 0, -270075, 49950250]\) | \(46694890801/3920400\) | \(182910182400000000\) | \([2, 2]\) | \(294912\) | \(2.0541\) | |
| 39600.cn5 | 39600cx1 | \([0, 0, 0, 17925, 3582250]\) | \(13651919/126720\) | \(-5912248320000000\) | \([2]\) | \(147456\) | \(1.7075\) | \(\Gamma_0(N)\)-optimal |
| 39600.cn6 | 39600cx5 | \([0, 0, 0, 1781925, -1623077750]\) | \(13411719834479/32153832150\) | \(-1500169192790400000000\) | \([2]\) | \(1179648\) | \(2.7473\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.cn have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.cn do not have complex multiplication.Modular form 39600.2.a.cn
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
