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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 38640.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.y1 | 38640f1 | \([0, -1, 0, -3168796, 2172205120]\) | \(13745695765783090269904/148545140625\) | \(38027556000000\) | \([2]\) | \(491520\) | \(2.1766\) | \(\Gamma_0(N)\)-optimal |
| 38640.y2 | 38640f2 | \([0, -1, 0, -3166296, 2175801120]\) | \(-3428296927707108677476/11297617307290125\) | \(-11568760122665088000\) | \([2]\) | \(983040\) | \(2.5232\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.y have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.y do not have complex multiplication.Modular form 38640.2.a.y
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.
