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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 200277.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200277.s1 | 200277s5 | \([1, -1, 0, -11753973, 15513408306]\) | \(10206027697760497/5557167\) | \(97785509890219767\) | \([2]\) | \(6553600\) | \(2.5887\) | |
| 200277.s2 | 200277s3 | \([1, -1, 0, -738738, 239683455]\) | \(2533811507137/58110129\) | \(1022522554037236329\) | \([2, 2]\) | \(3276800\) | \(2.2421\) | |
| 200277.s3 | 200277s2 | \([1, -1, 0, -101493, -6930360]\) | \(6570725617/2614689\) | \(46008820154108889\) | \([2, 2]\) | \(1638400\) | \(1.8956\) | |
| 200277.s4 | 200277s1 | \([1, -1, 0, -88488, -10106181]\) | \(4354703137/1617\) | \(28453197374217\) | \([2]\) | \(819200\) | \(1.5490\) | \(\Gamma_0(N)\)-optimal |
| 200277.s5 | 200277s6 | \([1, -1, 0, 80577, 741595824]\) | \(3288008303/13504609503\) | \(-237630995454907572903\) | \([2]\) | \(6553600\) | \(2.5887\) | |
| 200277.s6 | 200277s4 | \([1, -1, 0, 327672, -50447691]\) | \(221115865823/190238433\) | \(-3347490217879255833\) | \([2]\) | \(3276800\) | \(2.2421\) |
Rank
sage: E.rank()
The elliptic curves in class 200277.s have rank \(0\).
Complex multiplication
The elliptic curves in class 200277.s do not have complex multiplication.Modular form 200277.2.a.s
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
