Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 9408.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.bq1 | 9408bl1 | \([0, 1, 0, -18440, -765066]\) | \(92100460096/20253807\) | \(152501768943552\) | \([2]\) | \(46080\) | \(1.4350\) | \(\Gamma_0(N)\)-optimal |
9408.bq2 | 9408bl2 | \([0, 1, 0, 41095, -4634841]\) | \(15926924096/28588707\) | \(-13776620707196928\) | \([2]\) | \(92160\) | \(1.7816\) |
Rank
sage: E.rank()
The elliptic curves in class 9408.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 9408.bq do not have complex multiplication.Modular form 9408.2.a.bq
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.