Show commands:
SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 426888.gl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.gl1 | 426888gl2 | \([0, 0, 0, -173019, 22992662]\) | \(2450086/441\) | \(103100878457837568\) | \([2]\) | \(2949120\) | \(1.9836\) | \(\Gamma_0(N)\)-optimal* |
426888.gl2 | 426888gl1 | \([0, 0, 0, 21021, 2075150]\) | \(8788/21\) | \(-2454782820424704\) | \([2]\) | \(1474560\) | \(1.6370\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 426888.gl have rank \(0\).
Complex multiplication
The elliptic curves in class 426888.gl do not have complex multiplication.Modular form 426888.2.a.gl
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.