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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 99450.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99450.cj1 | 99450cz1 | \([1, -1, 1, -147926255, -692456991753]\) | \(31427652507069423952801/654426190080\) | \(7454323321380000000\) | \([2]\) | \(9338880\) | \(3.1506\) | \(\Gamma_0(N)\)-optimal |
99450.cj2 | 99450cz2 | \([1, -1, 1, -147764255, -694049451753]\) | \(-31324512477868037557921/143427974919699600\) | \(-1633734276819703256250000\) | \([2]\) | \(18677760\) | \(3.4972\) |
Rank
sage: E.rank()
The elliptic curves in class 99450.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 99450.cj do not have complex multiplication.Modular form 99450.2.a.cj
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 LMFDB 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 LMFDB labels.