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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 11550.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.q1 | 11550k3 | \([1, 1, 0, -264000025, -1651136586875]\) | \(130231365028993807856757649/4753980000\) | \(74280937500000\) | \([2]\) | \(1474560\) | \(3.0799\) | |
| 11550.q2 | 11550k4 | \([1, 1, 0, -16808025, -24791074875]\) | \(33608860073906150870929/2466782226562500000\) | \(38543472290039062500000\) | \([2]\) | \(1474560\) | \(3.0799\) | |
| 11550.q3 | 11550k2 | \([1, 1, 0, -16500025, -25804086875]\) | \(31794905164720991157649/192099600000000\) | \(3001556250000000000\) | \([2, 2]\) | \(737280\) | \(2.7333\) | |
| 11550.q4 | 11550k1 | \([1, 1, 0, -1012025, -419254875]\) | \(-7336316844655213969/604492922880000\) | \(-9445201920000000000\) | \([2]\) | \(368640\) | \(2.3868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.q have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.q do not have complex multiplication.Modular form 11550.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
