Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 17850.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17850.bq1 | 17850br2 | \([1, 0, 0, -9538, 357692]\) | \(6141556990297/1019592\) | \(15931125000\) | \([2]\) | \(24576\) | \(0.96562\) | |
17850.bq2 | 17850br1 | \([1, 0, 0, -538, 6692]\) | \(-1102302937/616896\) | \(-9639000000\) | \([2]\) | \(12288\) | \(0.61905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17850.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 17850.bq do not have complex multiplication.Modular form 17850.2.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.