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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 50430.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50430.h1 | 50430h1 | \([1, 1, 0, -88287, -3301839]\) | \(16022066761/8302500\) | \(39437740460902500\) | \([2]\) | \(430080\) | \(1.8764\) | \(\Gamma_0(N)\)-optimal |
50430.h2 | 50430h2 | \([1, 1, 0, 331963, -25238889]\) | \(851701809239/551452050\) | \(-2619454721413144050\) | \([2]\) | \(860160\) | \(2.2230\) |
Rank
sage: E.rank()
The elliptic curves in class 50430.h have rank \(0\).
Complex multiplication
The elliptic curves in class 50430.h do not have complex multiplication.Modular form 50430.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.