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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1350.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1350.h1 | 1350f2 | \([1, -1, 0, -717, -7309]\) | \(-132651/2\) | \(-615093750\) | \([]\) | \(648\) | \(0.48951\) | |
1350.h2 | 1350f3 | \([1, -1, 0, -342, 3316]\) | \(-1167051/512\) | \(-1944000000\) | \([]\) | \(648\) | \(0.48951\) | |
1350.h3 | 1350f1 | \([1, -1, 0, 33, -59]\) | \(9261/8\) | \(-3375000\) | \([]\) | \(216\) | \(-0.059792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.h have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.h do not have complex multiplication.Modular form 1350.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.