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SageMath
E = EllipticCurve("gf1")
E.isogeny_class()
Elliptic curves in class 52800.gf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.gf1 | 52800cs1 | \([0, 1, 0, -93, 333]\) | \(-56197120/3267\) | \(-5227200\) | \([]\) | \(10368\) | \(0.045363\) | \(\Gamma_0(N)\)-optimal |
| 52800.gf2 | 52800cs2 | \([0, 1, 0, 507, 813]\) | \(8990228480/5314683\) | \(-8503492800\) | \([]\) | \(31104\) | \(0.59467\) |
Rank
sage: E.rank()
The elliptic curves in class 52800.gf have rank \(1\).
Complex multiplication
The elliptic curves in class 52800.gf do not have complex multiplication.Modular form 52800.2.a.gf
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.
