Show commands:
SageMath
E = EllipticCurve("oy1")
E.isogeny_class()
Elliptic curves in class 141120oy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.c2 | 141120oy1 | \([0, 0, 0, -12348, -268912]\) | \(11664/5\) | \(89255722106880\) | \([2]\) | \(458752\) | \(1.3733\) | \(\Gamma_0(N)\)-optimal |
| 141120.c1 | 141120oy2 | \([0, 0, 0, -94668, 11025392]\) | \(1314036/25\) | \(1785114442137600\) | \([2]\) | \(917504\) | \(1.7199\) |
Rank
sage: E.rank()
The elliptic curves in class 141120oy have rank \(0\).
Complex multiplication
The elliptic curves in class 141120oy do not have complex multiplication.Modular form 141120.2.a.oy
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.
