Show commands:
SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 5610bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.bl2 | 5610bk1 | \([1, 0, 0, -880, 4352]\) | \(75370704203521/35157196800\) | \(35157196800\) | \([2]\) | \(5376\) | \(0.71804\) | \(\Gamma_0(N)\)-optimal |
5610.bl1 | 5610bk2 | \([1, 0, 0, -11760, 489600]\) | \(179865548102096641/119964240000\) | \(119964240000\) | \([2]\) | \(10752\) | \(1.0646\) |
Rank
sage: E.rank()
The elliptic curves in class 5610bk have rank \(1\).
Complex multiplication
The elliptic curves in class 5610bk do not have complex multiplication.Modular form 5610.2.a.bk
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.