Show commands:
SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 1587600.hy
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 1587600.hy1 | \([0, 0, 0, -39723075, 96779765250]\) | \(-15590912409/78125\) | \(-34735279005000000000000\) | \([]\) | \(127733760\) | \(3.1725\) |
| 1587600.hy2 | \([0, 0, 0, -33075, -71772750]\) | \(-9/5\) | \(-2223057856320000000\) | \([]\) | \(18247680\) | \(2.1995\) |
Rank
sage: E.rank()
The elliptic curves in class 1587600.hy have rank \(0\).
Complex multiplication
The elliptic curves in class 1587600.hy do not have complex multiplication.Modular form 1587600.2.a.hy
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
