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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 149058gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.dh3 | 149058gh1 | \([1, -1, 0, -199341, -34163375]\) | \(4649101309/6804\) | \(1282065253962948\) | \([2]\) | \(921600\) | \(1.8006\) | \(\Gamma_0(N)\)-optimal |
| 149058.dh4 | 149058gh2 | \([1, -1, 0, -142011, -54263273]\) | \(-1680914269/5786802\) | \(-1090396498495487274\) | \([2]\) | \(1843200\) | \(2.1472\) | |
| 149058.dh1 | 149058gh3 | \([1, -1, 0, -5961006, 5601278164]\) | \(124318741396429/51631104\) | \(9728754330121602048\) | \([2]\) | \(4608000\) | \(2.6053\) | |
| 149058.dh2 | 149058gh4 | \([1, -1, 0, -5043726, 7383186292]\) | \(-75306487574989/81352871712\) | \(-15329172564970665526944\) | \([2]\) | \(9216000\) | \(2.9519\) |
Rank
sage: E.rank()
The elliptic curves in class 149058gh have rank \(0\).
Complex multiplication
The elliptic curves in class 149058gh do not have complex multiplication.Modular form 149058.2.a.gh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
