Show commands:
SageMath
E = EllipticCurve("po1")
E.isogeny_class()
Elliptic curves in class 348480.po
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.po1 | 348480po1 | \([0, 0, 0, -246972, 47240336]\) | \(104795188976/1875\) | \(29807585280000\) | \([2]\) | \(1966080\) | \(1.7124\) | \(\Gamma_0(N)\)-optimal |
| 348480.po2 | 348480po2 | \([0, 0, 0, -239052, 50411504]\) | \(-23758298924/3515625\) | \(-223556889600000000\) | \([2]\) | \(3932160\) | \(2.0590\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.po have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.po do not have complex multiplication.Modular form 348480.2.a.po
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
