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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 80688.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80688.bg1 | 80688x2 | \([0, 1, 0, -15587173920, 749024758284276]\) | \(-21525971829968662032241/11122195296\) | \(-216398180535336346976256\) | \([]\) | \(60480000\) | \(4.2450\) | |
| 80688.bg2 | 80688x1 | \([0, 1, 0, -4707360, 122765657076]\) | \(-592915705201/334302806016\) | \(-6504338131496148639154176\) | \([]\) | \(12096000\) | \(3.4403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80688.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 80688.bg do not have complex multiplication.Modular form 80688.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
