Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 16170.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16170.bw1 | 16170by1 | \([1, 0, 0, -244756, 46584236]\) | \(13782741913468081/701662500\) | \(82549891462500\) | \([2]\) | \(138240\) | \(1.7404\) | \(\Gamma_0(N)\)-optimal |
16170.bw2 | 16170by2 | \([1, 0, 0, -231526, 51847130]\) | \(-11666347147400401/3126621093750\) | \(-367843845058593750\) | \([2]\) | \(276480\) | \(2.0869\) |
Rank
sage: E.rank()
The elliptic curves in class 16170.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 16170.bw do not have complex multiplication.Modular form 16170.2.a.bw
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.