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SageMath
E = EllipticCurve("jp1")
E.isogeny_class()
Elliptic curves in class 206400jp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.cj4 | 206400jp1 | \([0, -1, 0, 2367, 403137]\) | \(357911/17415\) | \(-71331840000000\) | \([2]\) | \(540672\) | \(1.3379\) | \(\Gamma_0(N)\)-optimal |
206400.cj3 | 206400jp2 | \([0, -1, 0, -69633, 6811137]\) | \(9116230969/416025\) | \(1704038400000000\) | \([2, 2]\) | \(1081344\) | \(1.6845\) | |
206400.cj1 | 206400jp3 | \([0, -1, 0, -1101633, 445411137]\) | \(36097320816649/80625\) | \(330240000000000\) | \([2]\) | \(2162688\) | \(2.0311\) | |
206400.cj2 | 206400jp4 | \([0, -1, 0, -189633, -22828863]\) | \(184122897769/51282015\) | \(210051133440000000\) | \([2]\) | \(2162688\) | \(2.0311\) |
Rank
sage: E.rank()
The elliptic curves in class 206400jp have rank \(0\).
Complex multiplication
The elliptic curves in class 206400jp do not have complex multiplication.Modular form 206400.2.a.jp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.