Show commands:
SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 15600bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bh2 | 15600bu1 | \([0, -1, 0, -3559208, 2585676912]\) | \(623295446073461/5458752\) | \(43670016000000000\) | \([2]\) | \(368640\) | \(2.3598\) | \(\Gamma_0(N)\)-optimal |
| 15600.bh1 | 15600bu2 | \([0, -1, 0, -3639208, 2463436912]\) | \(666276475992821/58199166792\) | \(465593334336000000000\) | \([2]\) | \(737280\) | \(2.7064\) |
Rank
sage: E.rank()
The elliptic curves in class 15600bu have rank \(1\).
Complex multiplication
The elliptic curves in class 15600bu do not have complex multiplication.Modular form 15600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
