Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 116928.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116928.em1 | 116928cb2 | \([0, 0, 0, -89004, -10220240]\) | \(408023180713/1421\) | \(271557328896\) | \([2]\) | \(294912\) | \(1.4134\) | |
| 116928.em2 | 116928cb1 | \([0, 0, 0, -5484, -164432]\) | \(-95443993/5887\) | \(-1125023219712\) | \([2]\) | \(147456\) | \(1.0668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116928.em have rank \(1\).
Complex multiplication
The elliptic curves in class 116928.em do not have complex multiplication.Modular form 116928.2.a.em
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.
