Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 163350bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163350.hv2 | 163350bu1 | \([1, -1, 1, 22120, 16782747]\) | \(1601613/163840\) | \(-122450296320000000\) | \([]\) | \(1944000\) | \(1.9583\) | \(\Gamma_0(N)\)-optimal |
163350.hv1 | 163350bu2 | \([1, -1, 1, -4333880, 3474478747]\) | \(-16522921323/4000\) | \(-2179352197687500000\) | \([]\) | \(5832000\) | \(2.5076\) |
Rank
sage: E.rank()
The elliptic curves in class 163350bu have rank \(0\).
Complex multiplication
The elliptic curves in class 163350bu do not have complex multiplication.Modular form 163350.2.a.bu
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.