Show commands:
SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 100800.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.gh1 | 100800dp2 | \([0, 0, 0, -26220, 2296240]\) | \(-417267265/235298\) | \(-1124153701171200\) | \([]\) | \(414720\) | \(1.5912\) | |
| 100800.gh2 | 100800dp1 | \([0, 0, 0, 2580, -42320]\) | \(397535/392\) | \(-1872809164800\) | \([]\) | \(138240\) | \(1.0419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.gh do not have complex multiplication.Modular form 100800.2.a.gh
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.
