Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 7098.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7098.bb1 | 7098ba2 | \([1, 0, 0, -5158, -143014]\) | \(531373116625/2058\) | \(58778538\) | \([]\) | \(6048\) | \(0.70410\) | |
7098.bb2 | 7098ba1 | \([1, 0, 0, -88, -40]\) | \(2640625/1512\) | \(43184232\) | \([3]\) | \(2016\) | \(0.15479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7098.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.bb do not have complex multiplication.Modular form 7098.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.