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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 58667.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58667.h1 | 58667b2 | \([1, 0, 1, -44657, 3628515]\) | \(408023180713/1421\) | \(34299485549\) | \([2]\) | \(118272\) | \(1.2410\) | |
58667.h2 | 58667b1 | \([1, 0, 1, -2752, 58209]\) | \(-95443993/5887\) | \(-142097868703\) | \([2]\) | \(59136\) | \(0.89440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58667.h have rank \(0\).
Complex multiplication
The elliptic curves in class 58667.h do not have complex multiplication.Modular form 58667.2.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.