Show commands:
SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 203840fs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203840.ep1 | 203840fs1 | \([0, -1, 0, -93361, -10125135]\) | \(46689225424/3901625\) | \(7520621029376000\) | \([2]\) | \(1769472\) | \(1.7883\) | \(\Gamma_0(N)\)-optimal |
203840.ep2 | 203840fs2 | \([0, -1, 0, 98719, -46581919]\) | \(13799183324/129390625\) | \(-997633401856000000\) | \([2]\) | \(3538944\) | \(2.1349\) |
Rank
sage: E.rank()
The elliptic curves in class 203840fs have rank \(2\).
Complex multiplication
The elliptic curves in class 203840fs do not have complex multiplication.Modular form 203840.2.a.fs
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.