Show commands:
SageMath
E = EllipticCurve("ir1")
E.isogeny_class()
Elliptic curves in class 388080ir
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.ir1 | 388080ir1 | \([0, 0, 0, -182427, 27727434]\) | \(51603494067/4336640\) | \(56424188734341120\) | \([2]\) | \(2949120\) | \(1.9561\) | \(\Gamma_0(N)\)-optimal |
| 388080.ir2 | 388080ir2 | \([0, 0, 0, 193893, 127301706]\) | \(61958108493/573927200\) | \(-7467388727810457600\) | \([2]\) | \(5898240\) | \(2.3027\) |
Rank
sage: E.rank()
The elliptic curves in class 388080ir have rank \(2\).
Complex multiplication
The elliptic curves in class 388080ir do not have complex multiplication.Modular form 388080.2.a.ir
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.
