Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 1872.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.o1 | 1872a2 | \([0, 0, 0, -459, 2538]\) | \(530604/169\) | \(3406261248\) | \([2]\) | \(768\) | \(0.53286\) | |
| 1872.o2 | 1872a1 | \([0, 0, 0, 81, 270]\) | \(11664/13\) | \(-65505024\) | \([2]\) | \(384\) | \(0.18629\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.o have rank \(1\).
Complex multiplication
The elliptic curves in class 1872.o do not have complex multiplication.Modular form 1872.2.a.o
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.
