Show commands:
SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 450800.fk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.fk1 | 450800fk2 | \([0, -1, 0, -2283808, -1327665408]\) | \(109348914285625/1472\) | \(17733563187200\) | \([]\) | \(3919104\) | \(2.0991\) | |
450800.fk2 | 450800fk1 | \([0, -1, 0, -29808, -1592128]\) | \(243135625/48668\) | \(586315932876800\) | \([]\) | \(1306368\) | \(1.5498\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800.fk have rank \(0\).
Complex multiplication
The elliptic curves in class 450800.fk do not have complex multiplication.Modular form 450800.2.a.fk
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.