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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 47190.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.h1 | 47190h4 | \([1, 1, 0, -738828, -244742472]\) | \(25176685646263969/57915000\) | \(102599955315000\) | \([2]\) | \(552960\) | \(1.9320\) | |
| 47190.h2 | 47190h2 | \([1, 1, 0, -46708, -3746288]\) | \(6361447449889/294465600\) | \(521663772801600\) | \([2, 2]\) | \(276480\) | \(1.5854\) | |
| 47190.h3 | 47190h1 | \([1, 1, 0, -7988, 195408]\) | \(31824875809/8785920\) | \(15564793221120\) | \([2]\) | \(138240\) | \(1.2388\) | \(\Gamma_0(N)\)-optimal |
| 47190.h4 | 47190h3 | \([1, 1, 0, 25892, -14244248]\) | \(1083523132511/50179392120\) | \(-88895854083499320\) | \([2]\) | \(552960\) | \(1.9320\) |
Rank
sage: E.rank()
The elliptic curves in class 47190.h have rank \(1\).
Complex multiplication
The elliptic curves in class 47190.h do not have complex multiplication.Modular form 47190.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
