Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 170352.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
170352.by1 | 170352fy1 | \([0, 0, 0, -9126, 296595]\) | \(55296/7\) | \(10640681133264\) | \([2]\) | \(368640\) | \(1.2289\) | \(\Gamma_0(N)\)-optimal |
170352.by2 | 170352fy2 | \([0, 0, 0, 13689, 1542294]\) | \(11664/49\) | \(-1191756286925568\) | \([2]\) | \(737280\) | \(1.5754\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.by have rank \(0\).
Complex multiplication
The elliptic curves in class 170352.by do not have complex multiplication.Modular form 170352.2.a.by
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.