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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 77658ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77658.z2 | 77658ba1 | \([1, 1, 1, -1674308, -871435195]\) | \(-82114348569625/4294176768\) | \(-27145050347109445632\) | \([2]\) | \(2128896\) | \(2.4885\) | \(\Gamma_0(N)\)-optimal |
77658.z1 | 77658ba2 | \([1, 1, 1, -27116548, -54361200571]\) | \(348831893748633625/884737728\) | \(5592748381835412672\) | \([2]\) | \(4257792\) | \(2.8351\) |
Rank
sage: E.rank()
The elliptic curves in class 77658ba have rank \(0\).
Complex multiplication
The elliptic curves in class 77658ba do not have complex multiplication.Modular form 77658.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.