Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 355740.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.k1 | 355740k2 | \([0, -1, 0, -3203636, -163250184]\) | \(68150496976/39220335\) | \(2092645265558504912640\) | \([2]\) | \(19906560\) | \(2.7807\) | |
| 355740.k2 | 355740k1 | \([0, -1, 0, 798439, -20776314]\) | \(16880451584/9823275\) | \(-32758245692300343600\) | \([2]\) | \(9953280\) | \(2.4341\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 355740.k have rank \(0\).
Complex multiplication
The elliptic curves in class 355740.k do not have complex multiplication.Modular form 355740.2.a.k
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.
