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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 241332f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
241332.f1 | 241332f1 | \([0, -1, 0, -57009, -5215146]\) | \(265327034368/297381\) | \(22966420595664\) | \([2]\) | \(691200\) | \(1.4778\) | \(\Gamma_0(N)\)-optimal |
241332.f2 | 241332f2 | \([0, -1, 0, -42644, -7921512]\) | \(-6940769488/18000297\) | \(-22242302863941888\) | \([2]\) | \(1382400\) | \(1.8244\) |
Rank
sage: E.rank()
The elliptic curves in class 241332f have rank \(1\).
Complex multiplication
The elliptic curves in class 241332f do not have complex multiplication.Modular form 241332.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.