Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 66240bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.c1 | 66240bo1 | \([0, 0, 0, -1668, -117592]\) | \(-687518464/7604375\) | \(-5676635520000\) | \([]\) | \(138240\) | \(1.1293\) | \(\Gamma_0(N)\)-optimal |
66240.c2 | 66240bo2 | \([0, 0, 0, 14892, 3035432]\) | \(489277573376/5615234375\) | \(-4191750000000000\) | \([]\) | \(414720\) | \(1.6786\) |
Rank
sage: E.rank()
The elliptic curves in class 66240bo have rank \(0\).
Complex multiplication
The elliptic curves in class 66240bo do not have complex multiplication.Modular form 66240.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.