Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 18480.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.s1 | 18480ca3 | \([0, -1, 0, -1549296, -741731904]\) | \(100407751863770656369/166028940000\) | \(680054538240000\) | \([2]\) | \(245760\) | \(2.1088\) | |
| 18480.s2 | 18480ca2 | \([0, -1, 0, -97776, -11327040]\) | \(25238585142450289/995844326400\) | \(4078978360934400\) | \([2, 2]\) | \(122880\) | \(1.7623\) | |
| 18480.s3 | 18480ca1 | \([0, -1, 0, -15856, 534976]\) | \(107639597521009/32699842560\) | \(133938555125760\) | \([2]\) | \(61440\) | \(1.4157\) | \(\Gamma_0(N)\)-optimal |
| 18480.s4 | 18480ca4 | \([0, -1, 0, 43024, -41401920]\) | \(2150235484224911/181905111732960\) | \(-745083337658204160\) | \([2]\) | \(245760\) | \(2.1088\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.s have rank \(0\).
Complex multiplication
The elliptic curves in class 18480.s do not have complex multiplication.Modular form 18480.2.a.s
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.
