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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1260f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1260.e1 | 1260f1 | \([0, 0, 0, -5088, -139687]\) | \(1248870793216/42525\) | \(496011600\) | \([2]\) | \(960\) | \(0.76020\) | \(\Gamma_0(N)\)-optimal |
1260.e2 | 1260f2 | \([0, 0, 0, -4863, -152602]\) | \(-68150496976/14467005\) | \(-2699890341120\) | \([2]\) | \(1920\) | \(1.1068\) |
Rank
sage: E.rank()
The elliptic curves in class 1260f have rank \(0\).
Complex multiplication
The elliptic curves in class 1260f do not have complex multiplication.Modular form 1260.2.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.