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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 23826r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23826.u4 | 23826r1 | \([1, 0, 1, -730, -196]\) | \(912673/528\) | \(24840225168\) | \([2]\) | \(27648\) | \(0.68412\) | \(\Gamma_0(N)\)-optimal |
23826.u2 | 23826r2 | \([1, 0, 1, -7950, 271276]\) | \(1180932193/4356\) | \(204931857636\) | \([2, 2]\) | \(55296\) | \(1.0307\) | |
23826.u3 | 23826r3 | \([1, 0, 1, -4340, 519644]\) | \(-192100033/2371842\) | \(-111585396482802\) | \([2]\) | \(110592\) | \(1.3773\) | |
23826.u1 | 23826r4 | \([1, 0, 1, -127080, 17425996]\) | \(4824238966273/66\) | \(3105028146\) | \([2]\) | \(110592\) | \(1.3773\) |
Rank
sage: E.rank()
The elliptic curves in class 23826r have rank \(1\).
Complex multiplication
The elliptic curves in class 23826r do not have complex multiplication.Modular form 23826.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.