Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 20808.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20808.j1 | 20808m1 | \([0, 0, 0, -11271, -186694]\) | \(35152/17\) | \(76579044509952\) | \([2]\) | \(55296\) | \(1.3577\) | \(\Gamma_0(N)\)-optimal |
| 20808.j2 | 20808m2 | \([0, 0, 0, 40749, -1424770]\) | \(415292/289\) | \(-5207375026676736\) | \([2]\) | \(110592\) | \(1.7043\) |
Rank
sage: E.rank()
The elliptic curves in class 20808.j have rank \(0\).
Complex multiplication
The elliptic curves in class 20808.j do not have complex multiplication.Modular form 20808.2.a.j
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 LMFDB 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 LMFDB labels.
