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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 272832f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272832.f2 | 272832f1 | \([0, -1, 0, 141055, -18091359]\) | \(10063705679/10384668\) | \(-320273332445380608\) | \([2]\) | \(5308416\) | \(2.0458\) | \(\Gamma_0(N)\)-optimal |
272832.f1 | 272832f2 | \([0, -1, 0, -768385, -166330079]\) | \(1626794704081/552715002\) | \(17046272021704998912\) | \([2]\) | \(10616832\) | \(2.3924\) |
Rank
sage: E.rank()
The elliptic curves in class 272832f have rank \(1\).
Complex multiplication
The elliptic curves in class 272832f do not have complex multiplication.Modular form 272832.2.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.