Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 68400.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.bw1 | 68400dh2 | \([0, 0, 0, -159675, -13641750]\) | \(260549802603/104256800\) | \(180155750400000000\) | \([2]\) | \(737280\) | \(2.0092\) | |
68400.bw2 | 68400dh1 | \([0, 0, 0, 32325, -1545750]\) | \(2161700757/1848320\) | \(-3193896960000000\) | \([2]\) | \(368640\) | \(1.6626\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68400.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 68400.bw do not have complex multiplication.Modular form 68400.2.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.