Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 9600.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9600.bq1 | 9600y2 | \([0, 1, 0, -3833, 89463]\) | \(389344/3\) | \(48000000000\) | \([2]\) | \(7680\) | \(0.87858\) | |
9600.bq2 | 9600y1 | \([0, 1, 0, -83, 3213]\) | \(-128/9\) | \(-4500000000\) | \([2]\) | \(3840\) | \(0.53201\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9600.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 9600.bq do not have complex multiplication.Modular form 9600.2.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.