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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 4830.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4830.bf1 | 4830be4 | \([1, 0, 0, -129836, -18017790]\) | \(242052349717010282689/167676468750\) | \(167676468750\) | \([2]\) | \(20736\) | \(1.4680\) | |
| 4830.bf2 | 4830be3 | \([1, 0, 0, -8166, -278304]\) | \(60221998378106209/1554376834500\) | \(1554376834500\) | \([2]\) | \(10368\) | \(1.1214\) | |
| 4830.bf3 | 4830be2 | \([1, 0, 0, -1946, -13524]\) | \(815016062816929/394524156600\) | \(394524156600\) | \([6]\) | \(6912\) | \(0.91865\) | |
| 4830.bf4 | 4830be1 | \([1, 0, 0, -1026, 12420]\) | \(119451676585249/1567702080\) | \(1567702080\) | \([6]\) | \(3456\) | \(0.57208\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 4830.bf do not have complex multiplication.Modular form 4830.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
