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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 8400.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8400.bx1 | 8400r3 | \([0, 1, 0, -3808, -91612]\) | \(381775972/567\) | \(9072000000\) | \([2]\) | \(8192\) | \(0.81168\) | |
| 8400.bx2 | 8400r2 | \([0, 1, 0, -308, -612]\) | \(810448/441\) | \(1764000000\) | \([2, 2]\) | \(4096\) | \(0.46510\) | |
| 8400.bx3 | 8400r1 | \([0, 1, 0, -183, 888]\) | \(2725888/21\) | \(5250000\) | \([2]\) | \(2048\) | \(0.11853\) | \(\Gamma_0(N)\)-optimal |
| 8400.bx4 | 8400r4 | \([0, 1, 0, 1192, -3612]\) | \(11696828/7203\) | \(-115248000000\) | \([2]\) | \(8192\) | \(0.81168\) |
Rank
sage: E.rank()
The elliptic curves in class 8400.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 8400.bx do not have complex multiplication.Modular form 8400.2.a.bx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
