Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 86190j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.e1 | 86190j1 | \([1, 1, 0, -198, -1152]\) | \(393832837/3060\) | \(6722820\) | \([2]\) | \(24576\) | \(0.13879\) | \(\Gamma_0(N)\)-optimal |
86190.e2 | 86190j2 | \([1, 1, 0, -68, -2478]\) | \(-16194277/1170450\) | \(-2571478650\) | \([2]\) | \(49152\) | \(0.48536\) |
Rank
sage: E.rank()
The elliptic curves in class 86190j have rank \(2\).
Complex multiplication
The elliptic curves in class 86190j do not have complex multiplication.Modular form 86190.2.a.j
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 Cremona 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 Cremona labels.