Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 235248.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235248.bw1 | 235248bw2 | \([0, -1, 0, -17605800, 28522635504]\) | \(-30526075007211889/103499257854\) | \(-2046243427545120301056\) | \([]\) | \(11063808\) | \(2.9533\) | |
235248.bw2 | 235248bw1 | \([0, -1, 0, -2760, -19274256]\) | \(-117649/8118144\) | \(-160500656220143616\) | \([]\) | \(1580544\) | \(1.9803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235248.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 235248.bw do not have complex multiplication.Modular form 235248.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.