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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 83790.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.h1 | 83790f2 | \([1, -1, 0, -1723078590, 27530401073300]\) | \(-244320235433784441003267/10427200000\) | \(-24146113416062400000\) | \([]\) | \(33592320\) | \(3.6522\) | |
83790.h2 | 83790f1 | \([1, -1, 0, -21094215, 38433663925]\) | \(-326784782222946131643/11721923828125000\) | \(-37234960644287109375000\) | \([]\) | \(11197440\) | \(3.1029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.h have rank \(0\).
Complex multiplication
The elliptic curves in class 83790.h do not have complex multiplication.Modular form 83790.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.