Show commands:
SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 95550.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.du1 | 95550fs1 | \([1, 0, 1, -446696276, 3633809548898]\) | \(-134057911417971280740025/1872\) | \(-137649330000\) | \([]\) | \(11088000\) | \(3.1170\) | \(\Gamma_0(N)\)-optimal |
95550.du2 | 95550fs2 | \([1, 0, 1, -435246201, 3828914507548]\) | \(-198417696411528597145/22989483914821632\) | \(-1056519450427675852800000000\) | \([]\) | \(55440000\) | \(3.9217\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.du have rank \(1\).
Complex multiplication
The elliptic curves in class 95550.du do not have complex multiplication.Modular form 95550.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.