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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 83790.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.i1 | 83790ba2 | \([1, -1, 0, -850410360, 9541258321216]\) | \(272011766516966956291165927/141259766579735040000\) | \(35321580853963007546880000\) | \([2]\) | \(38338560\) | \(3.8531\) | |
83790.i2 | 83790ba1 | \([1, -1, 0, -44010360, 202017361216]\) | \(-37702212117675062365927/48682087219200000000\) | \(-12172809862899302400000000\) | \([2]\) | \(19169280\) | \(3.5065\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.i have rank \(1\).
Complex multiplication
The elliptic curves in class 83790.i do not have complex multiplication.Modular form 83790.2.a.i
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.