Show commands:
SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 286650.hi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.hi1 | 286650hi1 | \([1, -1, 0, -13216842, 4248323316]\) | \(65352943209688399/35827476332544\) | \(139977390226931712000000\) | \([2]\) | \(38338560\) | \(3.1320\) | \(\Gamma_0(N)\)-optimal |
| 286650.hi2 | 286650hi2 | \([1, -1, 0, 51295158, 33472259316]\) | \(3820420340137317041/2334869460099072\) | \(-9122298498271760256000000\) | \([2]\) | \(76677120\) | \(3.4786\) |
Rank
sage: E.rank()
The elliptic curves in class 286650.hi have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.hi do not have complex multiplication.Modular form 286650.2.a.hi
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.
