Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 16900l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16900.o2 | 16900l1 | \([0, -1, 0, -108, -1288]\) | \(-208\) | \(-676000000\) | \([]\) | \(6480\) | \(0.37887\) | \(\Gamma_0(N)\)-optimal |
| 16900.o1 | 16900l2 | \([0, -1, 0, -13108, -573288]\) | \(-368484688\) | \(-676000000\) | \([]\) | \(19440\) | \(0.92817\) |
Rank
sage: E.rank()
The elliptic curves in class 16900l have rank \(0\).
Complex multiplication
The elliptic curves in class 16900l do not have complex multiplication.Modular form 16900.2.a.l
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.
