Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 289800x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.x2 | 289800x1 | \([0, 0, 0, -592275, -175441250]\) | \(1969910093092/7889\) | \(92017296000000\) | \([2]\) | \(1474560\) | \(1.8908\) | \(\Gamma_0(N)\)-optimal |
| 289800.x1 | 289800x2 | \([0, 0, 0, -601275, -169834250]\) | \(1030541881826/62236321\) | \(1451848896288000000\) | \([2]\) | \(2949120\) | \(2.2374\) |
Rank
sage: E.rank()
The elliptic curves in class 289800x have rank \(0\).
Complex multiplication
The elliptic curves in class 289800x do not have complex multiplication.Modular form 289800.2.a.x
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 Cremona 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 Cremona labels.
