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SageMath
sage: E = EllipticCurve("h1")
sage: E.isogeny_class()
Elliptic curves in class 38115.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 38115.h1 | 38115m6 | [1, -1, 1, -3320578823, -73648500528094] | [2] | 7372800 | |
| 38115.h2 | 38115m4 | [1, -1, 1, -207536198, -1150718660044] | [2, 2] | 3686400 | |
| 38115.h3 | 38115m5 | [1, -1, 1, -206507093, -1162696207318] | [2] | 7372800 | |
| 38115.h4 | 38115m3 | [1, -1, 1, -27709628, 29613639872] | [2] | 3686400 | |
| 38115.h5 | 38115m2 | [1, -1, 1, -13035353, -17790138088] | [2, 2] | 1843200 | |
| 38115.h6 | 38115m1 | [1, -1, 1, 38092, -831265234] | [2] | 921600 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38115.h have rank \(1\).
Complex multiplication
The elliptic curves in class 38115.h do not have complex multiplication.Modular form 38115.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
