Show commands:
SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 233450cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
233450.cg2 | 233450cg1 | \([1, -1, 1, -1289530, 563959097]\) | \(-15177411906818559273/167619938752\) | \(-2619061543000000\) | \([2]\) | \(3538944\) | \(2.1123\) | \(\Gamma_0(N)\)-optimal |
233450.cg1 | 233450cg2 | \([1, -1, 1, -20632530, 36077707097]\) | \(62167173500157644301993/7582456\) | \(118475875000\) | \([2]\) | \(7077888\) | \(2.4588\) |
Rank
sage: E.rank()
The elliptic curves in class 233450cg have rank \(0\).
Complex multiplication
The elliptic curves in class 233450cg do not have complex multiplication.Modular form 233450.2.a.cg
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.