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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 15246f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.s2 | 15246f1 | \([1, -1, 0, -666, -21708]\) | \(-33698267/193536\) | \(-187787787264\) | \([2]\) | \(23040\) | \(0.84710\) | \(\Gamma_0(N)\)-optimal |
15246.s1 | 15246f2 | \([1, -1, 0, -16506, -810540]\) | \(512576216027/1143072\) | \(1109121618528\) | \([2]\) | \(46080\) | \(1.1937\) |
Rank
sage: E.rank()
The elliptic curves in class 15246f have rank \(0\).
Complex multiplication
The elliptic curves in class 15246f do not have complex multiplication.Modular form 15246.2.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.