Show commands:
SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 206400hy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.ko1 | 206400hy1 | \([0, 1, 0, -305633, 59860863]\) | \(770842973809/66873600\) | \(273914265600000000\) | \([2]\) | \(2949120\) | \(2.0867\) | \(\Gamma_0(N)\)-optimal |
206400.ko2 | 206400hy2 | \([0, 1, 0, 334367, 278100863]\) | \(1009328859791/8734528080\) | \(-35776627015680000000\) | \([2]\) | \(5898240\) | \(2.4333\) |
Rank
sage: E.rank()
The elliptic curves in class 206400hy have rank \(0\).
Complex multiplication
The elliptic curves in class 206400hy do not have complex multiplication.Modular form 206400.2.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 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.