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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 163254h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163254.dm2 | 163254h1 | \([1, 0, 0, -88, 255488]\) | \(-15625/5842368\) | \(-28199994443712\) | \([2]\) | \(368640\) | \(1.2597\) | \(\Gamma_0(N)\)-optimal |
163254.dm1 | 163254h2 | \([1, 0, 0, -60928, 5694584]\) | \(5182207647625/91449288\) | \(441408246361992\) | \([2]\) | \(737280\) | \(1.6063\) |
Rank
sage: E.rank()
The elliptic curves in class 163254h have rank \(1\).
Complex multiplication
The elliptic curves in class 163254h do not have complex multiplication.Modular form 163254.2.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.