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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 160080.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160080.k1 | 160080bw1 | \([0, -1, 0, -443576, -109601424]\) | \(2356507705137010489/93358656000000\) | \(382397054976000000\) | \([2]\) | \(1935360\) | \(2.1405\) | \(\Gamma_0(N)\)-optimal |
160080.k2 | 160080bw2 | \([0, -1, 0, 196424, -400417424]\) | \(204618645563149511/17023122363528000\) | \(-69726709201010688000\) | \([2]\) | \(3870720\) | \(2.4871\) |
Rank
sage: E.rank()
The elliptic curves in class 160080.k have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.k do not have complex multiplication.Modular form 160080.2.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 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.