Show commands:
SageMath
E = EllipticCurve("pl1")
E.isogeny_class()
Elliptic curves in class 100800.pl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.pl1 | 100800nt4 | \([0, 0, 0, -1008300, -389702000]\) | \(303735479048/105\) | \(39191040000000\) | \([2]\) | \(1179648\) | \(1.9642\) | |
| 100800.pl2 | 100800nt2 | \([0, 0, 0, -63300, -6032000]\) | \(601211584/11025\) | \(514382400000000\) | \([2, 2]\) | \(589824\) | \(1.6176\) | |
| 100800.pl3 | 100800nt1 | \([0, 0, 0, -8175, 142000]\) | \(82881856/36015\) | \(26254935000000\) | \([2]\) | \(294912\) | \(1.2710\) | \(\Gamma_0(N)\)-optimal |
| 100800.pl4 | 100800nt3 | \([0, 0, 0, -300, -17498000]\) | \(-8/354375\) | \(-132269760000000000\) | \([2]\) | \(1179648\) | \(1.9642\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.pl have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.pl do not have complex multiplication.Modular form 100800.2.a.pl
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.
