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SageMath
sage: E = EllipticCurve("38829.h1")
sage: E.isogeny_class()
Elliptic curves in class 38829.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 38829.h1 | 38829f6 | [1, 1, 0, -1449654, 671203533] | [2] | 322560 | |
| 38829.h2 | 38829f4 | [1, 1, 0, -90639, 10450440] | [2, 2] | 161280 | |
| 38829.h3 | 38829f3 | [1, 1, 0, -72149, -7444182] | [2] | 161280 | |
| 38829.h4 | 38829f5 | [1, 1, 0, -62904, 17001447] | [2] | 322560 | |
| 38829.h5 | 38829f2 | [1, 1, 0, -7434, 49815] | [2, 2] | 80640 | |
| 38829.h6 | 38829f1 | [1, 1, 0, 1811, 7288] | [2] | 40320 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38829.h have rank \(1\).
Modular form 38829.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
