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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 479808k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.k2 | 479808k1 | \([0, 0, 0, 888468, 62535760]\) | \(3449795831/2071552\) | \(-46574856959372034048\) | \([2]\) | \(17694720\) | \(2.4632\) | \(\Gamma_0(N)\)-optimal* |
479808.k1 | 479808k2 | \([0, 0, 0, -3627372, 505088080]\) | \(234770924809/130960928\) | \(2944404238400300777472\) | \([2]\) | \(35389440\) | \(2.8098\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808k have rank \(0\).
Complex multiplication
The elliptic curves in class 479808k do not have complex multiplication.Modular form 479808.2.a.k
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.