Show commands:
SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 229840.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229840.bf1 | 229840n1 | \([0, 0, 0, -47827, -1805934]\) | \(611960049/282880\) | \(5592710061752320\) | \([2]\) | \(1032192\) | \(1.7163\) | \(\Gamma_0(N)\)-optimal |
| 229840.bf2 | 229840n2 | \([0, 0, 0, 168493, -13617006]\) | \(26757728271/19536400\) | \(-386246538639769600\) | \([2]\) | \(2064384\) | \(2.0629\) |
Rank
sage: E.rank()
The elliptic curves in class 229840.bf have rank \(2\).
Complex multiplication
The elliptic curves in class 229840.bf do not have complex multiplication.Modular form 229840.2.a.bf
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.
