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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 159201bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159201.bi3 | 159201bh1 | \([1, -1, 0, -242118, 39687759]\) | \(389017/57\) | \(229991735176663257\) | \([2]\) | \(1658880\) | \(2.0563\) | \(\Gamma_0(N)\)-optimal |
| 159201.bi2 | 159201bh2 | \([1, -1, 0, -1038123, -367707600]\) | \(30664297/3249\) | \(13109528905069805649\) | \([2, 2]\) | \(3317760\) | \(2.4029\) | |
| 159201.bi4 | 159201bh3 | \([1, -1, 0, 1349892, -1813411881]\) | \(67419143/390963\) | \(-1577513311576733279763\) | \([2]\) | \(6635520\) | \(2.7495\) | |
| 159201.bi1 | 159201bh4 | \([1, -1, 0, -16162218, -25004858355]\) | \(115714886617/1539\) | \(6209776849769907939\) | \([2]\) | \(6635520\) | \(2.7495\) |
Rank
sage: E.rank()
The elliptic curves in class 159201bh have rank \(0\).
Complex multiplication
The elliptic curves in class 159201bh do not have complex multiplication.Modular form 159201.2.a.bh
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.
