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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 26400.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26400.bw1 | 26400cb4 | \([0, 1, 0, -13233, -590337]\) | \(4004529472/99\) | \(6336000000\) | \([2]\) | \(32768\) | \(0.98994\) | |
| 26400.bw2 | 26400cb3 | \([0, 1, 0, -3608, 73788]\) | \(649461896/72171\) | \(577368000000\) | \([2]\) | \(32768\) | \(0.98994\) | |
| 26400.bw3 | 26400cb1 | \([0, 1, 0, -858, -8712]\) | \(69934528/9801\) | \(9801000000\) | \([2, 2]\) | \(16384\) | \(0.64337\) | \(\Gamma_0(N)\)-optimal |
| 26400.bw4 | 26400cb2 | \([0, 1, 0, 1392, -44712]\) | \(37259704/131769\) | \(-1054152000000\) | \([2]\) | \(32768\) | \(0.98994\) |
Rank
sage: E.rank()
The elliptic curves in class 26400.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 26400.bw do not have complex multiplication.Modular form 26400.2.a.bw
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.
