Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 32368.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32368.u1 | 32368h2 | \([0, 0, 0, -37859, -1247902]\) | \(60698457/28322\) | \(2800124842876928\) | \([2]\) | \(110592\) | \(1.6585\) | |
32368.u2 | 32368h1 | \([0, 0, 0, 8381, -147390]\) | \(658503/476\) | \(-47060921729024\) | \([2]\) | \(55296\) | \(1.3119\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32368.u have rank \(0\).
Complex multiplication
The elliptic curves in class 32368.u do not have complex multiplication.Modular form 32368.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.