Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 705600.j
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.j1 | \([0, 0, 0, -22946700, 45921526000]\) | \(-77626969/8000\) | \(-137708828393472000000000\) | \([]\) | \(69672960\) | \(3.1794\) |
| 705600.j2 | \([0, 0, 0, 1749300, -62426000]\) | \(34391/20\) | \(-344272070983680000000\) | \([]\) | \(23224320\) | \(2.6301\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.j have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.j do not have complex multiplication.Modular form 705600.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
