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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 7200.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7200.bz1 | 7200bn2 | \([0, 0, 0, -108075, -13675250]\) | \(23937672968/45\) | \(262440000000\) | \([2]\) | \(24576\) | \(1.4463\) | |
| 7200.bz2 | 7200bn3 | \([0, 0, 0, -18075, 657250]\) | \(111980168/32805\) | \(191318760000000\) | \([2]\) | \(24576\) | \(1.4463\) | |
| 7200.bz3 | 7200bn1 | \([0, 0, 0, -6825, -209000]\) | \(48228544/2025\) | \(1476225000000\) | \([2, 2]\) | \(12288\) | \(1.0998\) | \(\Gamma_0(N)\)-optimal |
| 7200.bz4 | 7200bn4 | \([0, 0, 0, 3300, -776000]\) | \(85184/5625\) | \(-262440000000000\) | \([2]\) | \(24576\) | \(1.4463\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 7200.bz do not have complex multiplication.Modular form 7200.2.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.
