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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 72128bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.br2 | 72128bj1 | \([0, -1, 0, -43969, 922209]\) | \(304821217/164864\) | \(5084567237033984\) | \([2]\) | \(368640\) | \(1.7048\) | \(\Gamma_0(N)\)-optimal |
72128.br1 | 72128bj2 | \([0, -1, 0, -545729, 155163233]\) | \(582810602977/829472\) | \(25581728911327232\) | \([2]\) | \(737280\) | \(2.0513\) |
Rank
sage: E.rank()
The elliptic curves in class 72128bj have rank \(1\).
Complex multiplication
The elliptic curves in class 72128bj do not have complex multiplication.Modular form 72128.2.a.bj
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.