Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 129437.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129437.e1 | 129437d2 | \([1, 0, 1, -86607, 9048635]\) | \(15124197817/1294139\) | \(6147295152343499\) | \([2]\) | \(839040\) | \(1.7708\) | |
129437.e2 | 129437d1 | \([1, 0, 1, 5848, 653721]\) | \(4657463/41503\) | \(-197143576314223\) | \([2]\) | \(419520\) | \(1.4242\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129437.e have rank \(0\).
Complex multiplication
The elliptic curves in class 129437.e do not have complex multiplication.Modular form 129437.2.a.e
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.