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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 60984.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.bw1 | 60984bx4 | \([0, 0, 0, -273339, 54264870]\) | \(1707831108/26411\) | \(34927575581961216\) | \([2]\) | \(491520\) | \(1.9756\) | |
| 60984.bw2 | 60984bx2 | \([0, 0, 0, -33759, -1078110]\) | \(12869712/5929\) | \(1960221078579456\) | \([2, 2]\) | \(245760\) | \(1.6291\) | |
| 60984.bw3 | 60984bx1 | \([0, 0, 0, -28314, -1832787]\) | \(121485312/77\) | \(1591088537808\) | \([2]\) | \(122880\) | \(1.2825\) | \(\Gamma_0(N)\)-optimal |
| 60984.bw4 | 60984bx3 | \([0, 0, 0, 118701, -8121762]\) | \(139863132/102487\) | \(-135535286004636672\) | \([2]\) | \(491520\) | \(1.9756\) |
Rank
sage: E.rank()
The elliptic curves in class 60984.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 60984.bw do not have complex multiplication.Modular form 60984.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
