Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 47610.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.bw1 | 47610cn2 | \([1, -1, 1, -1154642, -477042141]\) | \(1577505447721/838350\) | \(90473192018956350\) | \([2]\) | \(1216512\) | \(2.2034\) | |
47610.bw2 | 47610cn1 | \([1, -1, 1, -59612, -10121349]\) | \(-217081801/285660\) | \(-30827902465718460\) | \([2]\) | \(608256\) | \(1.8568\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47610.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 47610.bw do not have complex multiplication.Modular form 47610.2.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.