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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 5544.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5544.u1 | 5544j3 | \([0, 0, 0, -2259, -40770]\) | \(1707831108/26411\) | \(19715705856\) | \([2]\) | \(4096\) | \(0.77669\) | |
5544.u2 | 5544j2 | \([0, 0, 0, -279, 810]\) | \(12869712/5929\) | \(1106493696\) | \([2, 2]\) | \(2048\) | \(0.43011\) | |
5544.u3 | 5544j1 | \([0, 0, 0, -234, 1377]\) | \(121485312/77\) | \(898128\) | \([2]\) | \(1024\) | \(0.083538\) | \(\Gamma_0(N)\)-optimal |
5544.u4 | 5544j4 | \([0, 0, 0, 981, 6102]\) | \(139863132/102487\) | \(-76506135552\) | \([2]\) | \(4096\) | \(0.77669\) |
Rank
sage: E.rank()
The elliptic curves in class 5544.u have rank \(0\).
Complex multiplication
The elliptic curves in class 5544.u do not have complex multiplication.Modular form 5544.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.