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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3850f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3850.f4 | 3850f1 | \([1, -1, 0, -92, -11184]\) | \(-5545233/3469312\) | \(-54208000000\) | \([2]\) | \(3072\) | \(0.73874\) | \(\Gamma_0(N)\)-optimal |
| 3850.f3 | 3850f2 | \([1, -1, 0, -8092, -275184]\) | \(3750606459153/45914176\) | \(717409000000\) | \([2, 2]\) | \(6144\) | \(1.0853\) | |
| 3850.f1 | 3850f3 | \([1, -1, 0, -129092, -17820184]\) | \(15226621995131793/2324168\) | \(36315125000\) | \([2]\) | \(12288\) | \(1.4319\) | |
| 3850.f2 | 3850f4 | \([1, -1, 0, -15092, 277816]\) | \(24331017010833/12004097336\) | \(187564020875000\) | \([2]\) | \(12288\) | \(1.4319\) |
Rank
sage: E.rank()
The elliptic curves in class 3850f have rank \(0\).
Complex multiplication
The elliptic curves in class 3850f do not have complex multiplication.Modular form 3850.2.a.f
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.
