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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 259920.gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.gc1 | 259920gc2 | \([0, 0, 0, -1340200587, -18881903956934]\) | \(276288773643091/41990400\) | \(40459442720822417188454400\) | \([2]\) | \(74711040\) | \(3.9261\) | |
| 259920.gc2 | 259920gc1 | \([0, 0, 0, -75949707, -352284509126]\) | \(-50284268371/26542080\) | \(-25574363793902564938874880\) | \([2]\) | \(37355520\) | \(3.5795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.gc have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.gc do not have complex multiplication.Modular form 259920.2.a.gc
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.
