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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 258f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258.f2 | 258f1 | \([1, 0, 0, 159, 1737]\) | \(444369620591/1540767744\) | \(-1540767744\) | \([7]\) | \(168\) | \(0.44597\) | \(\Gamma_0(N)\)-optimal |
258.f1 | 258f2 | \([1, 0, 0, -59901, -5648523]\) | \(-23769846831649063249/3261823333284\) | \(-3261823333284\) | \([]\) | \(1176\) | \(1.4189\) |
Rank
sage: E.rank()
The elliptic curves in class 258f have rank \(0\).
Complex multiplication
The elliptic curves in class 258f do not have complex multiplication.Modular form 258.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.