Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 9576bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.q2 | 9576bb1 | \([0, 0, 0, -390, 3197]\) | \(-562432000/53067\) | \(-618973488\) | \([2]\) | \(3072\) | \(0.42887\) | \(\Gamma_0(N)\)-optimal |
| 9576.q1 | 9576bb2 | \([0, 0, 0, -6375, 195914]\) | \(153531250000/1197\) | \(223388928\) | \([2]\) | \(6144\) | \(0.77545\) |
Rank
sage: E.rank()
The elliptic curves in class 9576bb have rank \(1\).
Complex multiplication
The elliptic curves in class 9576bb do not have complex multiplication.Modular form 9576.2.a.bb
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.
