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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 11550.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.d1 | 11550d3 | \([1, 1, 0, -606525, -182064375]\) | \(1579250141304807889/41926500\) | \(655101562500\) | \([2]\) | \(124416\) | \(1.7814\) | |
| 11550.d2 | 11550d4 | \([1, 1, 0, -605775, -182536125]\) | \(-1573398910560073969/8138108343750\) | \(-127157942871093750\) | \([2]\) | \(248832\) | \(2.1280\) | |
| 11550.d3 | 11550d1 | \([1, 1, 0, -8025, -214875]\) | \(3658671062929/880165440\) | \(13752585000000\) | \([2]\) | \(41472\) | \(1.2321\) | \(\Gamma_0(N)\)-optimal |
| 11550.d4 | 11550d2 | \([1, 1, 0, 18975, -1321875]\) | \(48351870250991/76871856600\) | \(-1201122759375000\) | \([2]\) | \(82944\) | \(1.5787\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.d have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.d do not have complex multiplication.Modular form 11550.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
