Show commands:
SageMath
E = EllipticCurve("ng1")
E.isogeny_class()
Elliptic curves in class 100800ng
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.ni2 | 100800ng1 | \([0, 0, 0, 23325, -2378000]\) | \(1925134784/4465125\) | \(-3255076125000000\) | \([2]\) | \(442368\) | \(1.6606\) | \(\Gamma_0(N)\)-optimal |
| 100800.ni1 | 100800ng2 | \([0, 0, 0, -189300, -26192000]\) | \(16079333824/2953125\) | \(137781000000000000\) | \([2]\) | \(884736\) | \(2.0072\) |
Rank
sage: E.rank()
The elliptic curves in class 100800ng have rank \(0\).
Complex multiplication
The elliptic curves in class 100800ng do not have complex multiplication.Modular form 100800.2.a.ng
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.
