Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 59150bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59150.bl2 | 59150bw1 | \([1, 1, 1, 757, 7041]\) | \(397535/392\) | \(-47302728200\) | \([]\) | \(55296\) | \(0.73530\) | \(\Gamma_0(N)\)-optimal |
59150.bl1 | 59150bw2 | \([1, 1, 1, -7693, -368139]\) | \(-417267265/235298\) | \(-28393462602050\) | \([]\) | \(165888\) | \(1.2846\) |
Rank
sage: E.rank()
The elliptic curves in class 59150bw have rank \(1\).
Complex multiplication
The elliptic curves in class 59150bw do not have complex multiplication.Modular form 59150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.