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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 29760.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29760.bz1 | 29760cj4 | \([0, 1, 0, -26561, -1674945]\) | \(15811147933922/1016955\) | \(133294325760\) | \([2]\) | \(49152\) | \(1.1922\) | |
| 29760.bz2 | 29760cj3 | \([0, 1, 0, -8961, 303615]\) | \(607199886722/41558445\) | \(5447148503040\) | \([2]\) | \(49152\) | \(1.1922\) | |
| 29760.bz3 | 29760cj2 | \([0, 1, 0, -1761, -23265]\) | \(9220796644/1946025\) | \(127534694400\) | \([2, 2]\) | \(24576\) | \(0.84561\) | |
| 29760.bz4 | 29760cj1 | \([0, 1, 0, 239, -2065]\) | \(91765424/174375\) | \(-2856960000\) | \([2]\) | \(12288\) | \(0.49904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29760.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 29760.bz do not have complex multiplication.Modular form 29760.2.a.bz
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.
