Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 6534o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6534.c2 | 6534o1 | \([1, -1, 0, -6, 6]\) | \(8019/2\) | \(6534\) | \([]\) | \(720\) | \(-0.55779\) | \(\Gamma_0(N)\)-optimal |
6534.c1 | 6534o2 | \([1, -1, 0, -171, -819]\) | \(18868971/8\) | \(235224\) | \([]\) | \(2160\) | \(-0.0084877\) |
Rank
sage: E.rank()
The elliptic curves in class 6534o have rank \(1\).
Complex multiplication
The elliptic curves in class 6534o do not have complex multiplication.Modular form 6534.2.a.o
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.