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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 18480.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.bx1 | 18480cq3 | \([0, 1, 0, -33976, 2373140]\) | \(1058993490188089/13182390375\) | \(53995070976000\) | \([2]\) | \(73728\) | \(1.4447\) | |
| 18480.bx2 | 18480cq2 | \([0, 1, 0, -3976, -38860]\) | \(1697509118089/833765625\) | \(3415104000000\) | \([2, 2]\) | \(36864\) | \(1.0982\) | |
| 18480.bx3 | 18480cq1 | \([0, 1, 0, -3256, -72556]\) | \(932288503609/779625\) | \(3193344000\) | \([2]\) | \(18432\) | \(0.75160\) | \(\Gamma_0(N)\)-optimal |
| 18480.bx4 | 18480cq4 | \([0, 1, 0, 14504, -282796]\) | \(82375335041831/56396484375\) | \(-231000000000000\) | \([2]\) | \(73728\) | \(1.4447\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.bx do not have complex multiplication.Modular form 18480.2.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.
