Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 208208bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
208208.g2 | 208208bw1 | \([0, 1, 0, 646876, -212067140]\) | \(24226243449392/29774625727\) | \(-36791406446263076608\) | \([2]\) | \(4515840\) | \(2.4404\) | \(\Gamma_0(N)\)-optimal |
208208.g1 | 208208bw2 | \([0, 1, 0, -3851904, -2042170844]\) | \(1278763167594532/375974556419\) | \(1858311549638898658304\) | \([2]\) | \(9031680\) | \(2.7870\) |
Rank
sage: E.rank()
The elliptic curves in class 208208bw have rank \(0\).
Complex multiplication
The elliptic curves in class 208208bw do not have complex multiplication.Modular form 208208.2.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 Cremona 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 Cremona labels.