Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 15600.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15600.y1 | 15600bh2 | \([0, -1, 0, -18408, 867312]\) | \(10779215329/1232010\) | \(78848640000000\) | \([2]\) | \(55296\) | \(1.3988\) | |
15600.y2 | 15600bh1 | \([0, -1, 0, 1592, 67312]\) | \(6967871/35100\) | \(-2246400000000\) | \([2]\) | \(27648\) | \(1.0522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.y have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.y do not have complex multiplication.Modular form 15600.2.a.y
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.