Show commands:
SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 100800.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.ct1 | 100800dl1 | \([0, 0, 0, -508800, -139687000]\) | \(1248870793216/42525\) | \(496011600000000\) | \([2]\) | \(737280\) | \(1.9115\) | \(\Gamma_0(N)\)-optimal |
100800.ct2 | 100800dl2 | \([0, 0, 0, -486300, -152602000]\) | \(-68150496976/14467005\) | \(-2699890341120000000\) | \([2]\) | \(1474560\) | \(2.2581\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.ct do not have complex multiplication.Modular form 100800.2.a.ct
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.