Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 8400by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8400.bj1 | 8400by1 | \([0, -1, 0, -288, -1728]\) | \(5177717/189\) | \(96768000\) | \([2]\) | \(3072\) | \(0.30193\) | \(\Gamma_0(N)\)-optimal |
| 8400.bj2 | 8400by2 | \([0, -1, 0, 112, -6528]\) | \(300763/35721\) | \(-18289152000\) | \([2]\) | \(6144\) | \(0.64850\) |
Rank
sage: E.rank()
The elliptic curves in class 8400by have rank \(0\).
Complex multiplication
The elliptic curves in class 8400by do not have complex multiplication.Modular form 8400.2.a.by
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.
