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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 7200.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7200.bx1 | 7200o2 | \([0, 0, 0, -7275, -238750]\) | \(7301384/3\) | \(17496000000\) | \([2]\) | \(8192\) | \(0.92780\) | |
| 7200.bx2 | 7200o3 | \([0, 0, 0, -3900, 92000]\) | \(140608/3\) | \(139968000000\) | \([2]\) | \(8192\) | \(0.92780\) | |
| 7200.bx3 | 7200o1 | \([0, 0, 0, -525, -2500]\) | \(21952/9\) | \(6561000000\) | \([2, 2]\) | \(4096\) | \(0.58123\) | \(\Gamma_0(N)\)-optimal |
| 7200.bx4 | 7200o4 | \([0, 0, 0, 1725, -18250]\) | \(97336/81\) | \(-472392000000\) | \([2]\) | \(8192\) | \(0.92780\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 7200.bx do not have complex multiplication.Modular form 7200.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
