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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 203280fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.ee4 | 203280fv1 | \([0, 1, 0, 44004, 3418380]\) | \(20777545136/23059575\) | \(-10457969599123200\) | \([2]\) | \(983040\) | \(1.7603\) | \(\Gamma_0(N)\)-optimal |
| 203280.ee3 | 203280fv2 | \([0, 1, 0, -248816, 31880484]\) | \(939083699236/300155625\) | \(544505855160960000\) | \([2, 2]\) | \(1966080\) | \(2.1069\) | |
| 203280.ee1 | 203280fv3 | \([0, 1, 0, -3602936, 2630652660]\) | \(1425631925916578/270703125\) | \(982153418400000000\) | \([2]\) | \(3932160\) | \(2.4535\) | |
| 203280.ee2 | 203280fv4 | \([0, 1, 0, -1579816, -740631916]\) | \(120186986927618/4332064275\) | \(15717409011882547200\) | \([2]\) | \(3932160\) | \(2.4535\) |
Rank
sage: E.rank()
The elliptic curves in class 203280fv have rank \(1\).
Complex multiplication
The elliptic curves in class 203280fv do not have complex multiplication.Modular form 203280.2.a.fv
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
