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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 59290h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.z2 | 59290h1 | \([1, -1, 0, -158230, 2136756]\) | \(6128487/3520\) | \(251640844824255040\) | \([2]\) | \(645120\) | \(2.0285\) | \(\Gamma_0(N)\)-optimal |
59290.z1 | 59290h2 | \([1, -1, 0, -1818350, 942096700]\) | \(9300746727/24200\) | \(1730030808166753400\) | \([2]\) | \(1290240\) | \(2.3751\) |
Rank
sage: E.rank()
The elliptic curves in class 59290h have rank \(1\).
Complex multiplication
The elliptic curves in class 59290h do not have complex multiplication.Modular form 59290.2.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 Cremona 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 Cremona labels.