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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 424830.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.du1 | 424830du1 | \([1, 0, 1, -9594373, 11749822256]\) | \(-5831629329001/186624000\) | \(-3125726859762710784000\) | \([3]\) | \(39261024\) | \(2.9003\) | \(\Gamma_0(N)\)-optimal |
424830.du2 | 424830du2 | \([1, 0, 1, 44571452, 43230999746]\) | \(584669638645799/386547056640\) | \(-6474196874474161428234240\) | \([]\) | \(117783072\) | \(3.4496\) |
Rank
sage: E.rank()
The elliptic curves in class 424830.du have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.du do not have complex multiplication.Modular form 424830.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.