Show commands:
SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 244800et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.et1 | 244800et1 | \([0, 0, 0, -36300, 1690000]\) | \(1771561/612\) | \(1827422208000000\) | \([2]\) | \(983040\) | \(1.6302\) | \(\Gamma_0(N)\)-optimal |
| 244800.et2 | 244800et2 | \([0, 0, 0, 107700, 11770000]\) | \(46268279/46818\) | \(-139797798912000000\) | \([2]\) | \(1966080\) | \(1.9768\) |
Rank
sage: E.rank()
The elliptic curves in class 244800et have rank \(1\).
Complex multiplication
The elliptic curves in class 244800et do not have complex multiplication.Modular form 244800.2.a.et
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.
