Show commands:
SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 170352.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170352.ff1 | 170352gi1 | \([0, 0, 0, -1014, -10985]\) | \(55296/7\) | \(14596270416\) | \([2]\) | \(122880\) | \(0.67955\) | \(\Gamma_0(N)\)-optimal |
170352.ff2 | 170352gi2 | \([0, 0, 0, 1521, -57122]\) | \(11664/49\) | \(-1634782286592\) | \([2]\) | \(245760\) | \(1.0261\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.ff have rank \(0\).
Complex multiplication
The elliptic curves in class 170352.ff do not have complex multiplication.Modular form 170352.2.a.ff
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.