Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 6720.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6720.ba1 | 6720bs2 | \([0, -1, 0, -105, -375]\) | \(31554496/525\) | \(2150400\) | \([2]\) | \(1536\) | \(0.013582\) | |
6720.ba2 | 6720bs1 | \([0, -1, 0, 0, -18]\) | \(-64/2205\) | \(-141120\) | \([2]\) | \(768\) | \(-0.33299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.ba do not have complex multiplication.Modular form 6720.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.