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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 23826.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23826.q1 | 23826n1 | \([1, 0, 1, -6522556, 6411180026]\) | \(-235484681972809299625/3345408\) | \(-435976915968\) | \([3]\) | \(453600\) | \(2.2405\) | \(\Gamma_0(N)\)-optimal |
23826.q2 | 23826n2 | \([1, 0, 1, -6484651, 6489385622]\) | \(-231403026519578265625/5706597418401792\) | \(-743689482163539935232\) | \([]\) | \(1360800\) | \(2.7898\) |
Rank
sage: E.rank()
The elliptic curves in class 23826.q have rank \(0\).
Complex multiplication
The elliptic curves in class 23826.q do not have complex multiplication.Modular form 23826.2.a.q
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.