Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 52800.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52800.bw1 | 52800bs1 | \([0, -1, 0, -2333, 46287]\) | \(-56197120/3267\) | \(-81675000000\) | \([]\) | \(51840\) | \(0.85008\) | \(\Gamma_0(N)\)-optimal |
52800.bw2 | 52800bs2 | \([0, -1, 0, 12667, 76287]\) | \(8990228480/5314683\) | \(-132867075000000\) | \([]\) | \(155520\) | \(1.3994\) |
Rank
sage: E.rank()
The elliptic curves in class 52800.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 52800.bw do not have complex multiplication.Modular form 52800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.