Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 166410.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.bu1 | 166410z4 | \([1, -1, 1, -2124848, 1192681531]\) | \(8527173507/200\) | \(24884677778693400\) | \([2]\) | \(3773952\) | \(2.2581\) | |
166410.bu2 | 166410z3 | \([1, -1, 1, -127928, 20090107]\) | \(-1860867/320\) | \(-39815484445909440\) | \([2]\) | \(1886976\) | \(1.9115\) | |
166410.bu3 | 166410z2 | \([1, -1, 1, -44723, -940419]\) | \(57960603/31250\) | \(5333650072593750\) | \([2]\) | \(1257984\) | \(1.7088\) | |
166410.bu4 | 166410z1 | \([1, -1, 1, 10747, -119463]\) | \(804357/500\) | \(-85338401161500\) | \([2]\) | \(628992\) | \(1.3622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 166410.bu do not have complex multiplication.Modular form 166410.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.