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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 23826m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23826.p2 | 23826m1 | \([1, 0, 1, -685186, -269272984]\) | \(-2094688437625/631351908\) | \(-10722604930573632228\) | \([3]\) | \(492480\) | \(2.3656\) | \(\Gamma_0(N)\)-optimal |
23826.p1 | 23826m2 | \([1, 0, 1, -59020981, -174529959808]\) | \(-1338795256993539625/20699712\) | \(-351554863682544192\) | \([]\) | \(1477440\) | \(2.9149\) |
Rank
sage: E.rank()
The elliptic curves in class 23826m have rank \(0\).
Complex multiplication
The elliptic curves in class 23826m do not have complex multiplication.Modular form 23826.2.a.m
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.