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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 81600.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81600.ce1 | 81600fh6 | \([0, -1, 0, -44390433, 113851468737]\) | \(2361739090258884097/5202\) | \(21307392000000\) | \([2]\) | \(3145728\) | \(2.6915\) | |
| 81600.ce2 | 81600fh4 | \([0, -1, 0, -2774433, 1779580737]\) | \(576615941610337/27060804\) | \(110841053184000000\) | \([2, 2]\) | \(1572864\) | \(2.3449\) | |
| 81600.ce3 | 81600fh5 | \([0, -1, 0, -2630433, 1972396737]\) | \(-491411892194497/125563633938\) | \(-514308644610048000000\) | \([2]\) | \(3145728\) | \(2.6915\) | |
| 81600.ce4 | 81600fh2 | \([0, -1, 0, -182433, 24796737]\) | \(163936758817/30338064\) | \(124264710144000000\) | \([2, 2]\) | \(786432\) | \(1.9984\) | |
| 81600.ce5 | 81600fh1 | \([0, -1, 0, -54433, -4515263]\) | \(4354703137/352512\) | \(1443889152000000\) | \([2]\) | \(393216\) | \(1.6518\) | \(\Gamma_0(N)\)-optimal |
| 81600.ce6 | 81600fh3 | \([0, -1, 0, 361567, 143932737]\) | \(1276229915423/2927177028\) | \(-11989717106688000000\) | \([2]\) | \(1572864\) | \(2.3449\) |
Rank
sage: E.rank()
The elliptic curves in class 81600.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 81600.ce do not have complex multiplication.Modular form 81600.2.a.ce
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
