Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 254100bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.bj2 | 254100bj1 | \([0, -1, 0, -185533, -30618938]\) | \(1594753024/4725\) | \(2092656431250000\) | \([2]\) | \(1866240\) | \(1.8096\) | \(\Gamma_0(N)\)-optimal |
| 254100.bj3 | 254100bj2 | \([0, -1, 0, -109908, -55877688]\) | \(-20720464/178605\) | \(-1265638609620000000\) | \([2]\) | \(3732480\) | \(2.1561\) | |
| 254100.bj1 | 254100bj3 | \([0, -1, 0, -911533, 309693562]\) | \(189123395584/16078125\) | \(7120844800781250000\) | \([2]\) | \(5598720\) | \(2.3589\) | |
| 254100.bj4 | 254100bj4 | \([0, -1, 0, 979092, 1425162312]\) | \(14647977776/132355125\) | \(-937900710400500000000\) | \([2]\) | \(11197440\) | \(2.7054\) |
Rank
sage: E.rank()
The elliptic curves in class 254100bj have rank \(0\).
Complex multiplication
The elliptic curves in class 254100bj do not have complex multiplication.Modular form 254100.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
