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SageMath
E = EllipticCurve("gt1")
E.isogeny_class()
Elliptic curves in class 52800.gt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.gt1 | 52800gd2 | \([0, 1, 0, -129233, -17924337]\) | \(932410994128/29403\) | \(7527168000000\) | \([2]\) | \(245760\) | \(1.5667\) | |
| 52800.gt2 | 52800gd1 | \([0, 1, 0, -7733, -306837]\) | \(-3196715008/649539\) | \(-10392624000000\) | \([2]\) | \(122880\) | \(1.2201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52800.gt have rank \(1\).
Complex multiplication
The elliptic curves in class 52800.gt do not have complex multiplication.Modular form 52800.2.a.gt
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.
