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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 206400.im
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206400.im1 | 206400bw4 | \([0, 1, 0, -1101633, -445411137]\) | \(36097320816649/80625\) | \(330240000000000\) | \([2]\) | \(2162688\) | \(2.0311\) | |
| 206400.im2 | 206400bw3 | \([0, 1, 0, -189633, 22828863]\) | \(184122897769/51282015\) | \(210051133440000000\) | \([2]\) | \(2162688\) | \(2.0311\) | |
| 206400.im3 | 206400bw2 | \([0, 1, 0, -69633, -6811137]\) | \(9116230969/416025\) | \(1704038400000000\) | \([2, 2]\) | \(1081344\) | \(1.6845\) | |
| 206400.im4 | 206400bw1 | \([0, 1, 0, 2367, -403137]\) | \(357911/17415\) | \(-71331840000000\) | \([2]\) | \(540672\) | \(1.3379\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.im have rank \(1\).
Complex multiplication
The elliptic curves in class 206400.im do not have complex multiplication.Modular form 206400.2.a.im
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
