Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 450840.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450840.bw1 | 450840bw1 | \([0, 1, 0, -1555596, -747299520]\) | \(330999787611942608/200201625\) | \(251799189408000\) | \([2]\) | \(5750784\) | \(2.0856\) | \(\Gamma_0(N)\)-optimal |
| 450840.bw2 | 450840bw2 | \([0, 1, 0, -1546416, -756545616]\) | \(-81293584906713092/2036310046875\) | \(-10244496650544000000\) | \([2]\) | \(11501568\) | \(2.4322\) |
Rank
sage: E.rank()
The elliptic curves in class 450840.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.bw do not have complex multiplication.Modular form 450840.2.a.bw
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.
