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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11550.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.h1 | 11550o1 | \([1, 1, 0, -2250, -42150]\) | \(-2016939204025/6764142\) | \(-4227588750\) | \([]\) | \(12000\) | \(0.71163\) | \(\Gamma_0(N)\)-optimal |
11550.h2 | 11550o2 | \([1, 1, 0, 16175, 827125]\) | \(1197993859655/1437603552\) | \(-561563887500000\) | \([]\) | \(60000\) | \(1.5163\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.h have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.h do not have complex multiplication.Modular form 11550.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.