Show commands:
SageMath
E = EllipticCurve("yo1")
E.isogeny_class()
Elliptic curves in class 235200yo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.yo1 | 235200yo1 | \([0, 1, 0, -534753, -149883777]\) | \(4386781853/27216\) | \(104921012109312000\) | \([2]\) | \(2949120\) | \(2.1040\) | \(\Gamma_0(N)\)-optimal |
235200.yo2 | 235200yo2 | \([0, 1, 0, -221153, -323931777]\) | \(-310288733/11573604\) | \(-44617660399484928000\) | \([2]\) | \(5898240\) | \(2.4506\) |
Rank
sage: E.rank()
The elliptic curves in class 235200yo have rank \(0\).
Complex multiplication
The elliptic curves in class 235200yo do not have complex multiplication.Modular form 235200.2.a.yo
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.