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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 48672bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48672.x2 | 48672bn1 | \([0, 0, 0, -27885, 1775176]\) | \(10648000/117\) | \(26348353282368\) | \([2]\) | \(86016\) | \(1.3899\) | \(\Gamma_0(N)\)-optimal |
| 48672.x1 | 48672bn2 | \([0, 0, 0, -50700, -1546688]\) | \(1000000/507\) | \(7307276643643392\) | \([2]\) | \(172032\) | \(1.7365\) |
Rank
sage: E.rank()
The elliptic curves in class 48672bn have rank \(1\).
Complex multiplication
The elliptic curves in class 48672bn do not have complex multiplication.Modular form 48672.2.a.bn
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
