Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 115542.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115542.u1 | 115542t2 | \([1, -1, 0, -100126854, -385607236694]\) | \(1294373635812597347281/2083292441154\) | \(178675911586399343634\) | \([]\) | \(11088000\) | \(3.1503\) | |
115542.u2 | 115542t1 | \([1, -1, 0, -941544, 334473376]\) | \(1076291879750641/60150618144\) | \(5158885193963099424\) | \([]\) | \(2217600\) | \(2.3456\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115542.u have rank \(0\).
Complex multiplication
The elliptic curves in class 115542.u do not have complex multiplication.Modular form 115542.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.