Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 96330bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96330.bm2 | 96330bm1 | \([1, 0, 1, -246068, -47217922]\) | \(-341370886042369/1817528220\) | \(-8772861570049980\) | \([2]\) | \(1075200\) | \(1.9040\) | \(\Gamma_0(N)\)-optimal |
96330.bm1 | 96330bm2 | \([1, 0, 1, -3942098, -3012912394]\) | \(1403607530712116449/39475350\) | \(190539974658150\) | \([2]\) | \(2150400\) | \(2.2505\) |
Rank
sage: E.rank()
The elliptic curves in class 96330bm have rank \(1\).
Complex multiplication
The elliptic curves in class 96330bm do not have complex multiplication.Modular form 96330.2.a.bm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.