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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 450840.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450840.bx1 | 450840bx1 | \([0, 1, 0, -892777451, -10267667754810]\) | \(203769809659907949070336/2016474841511325\) | \(778764809979898743502800\) | \([2]\) | \(145981440\) | \(3.7443\) | \(\Gamma_0(N)\)-optimal |
| 450840.bx2 | 450840bx2 | \([0, 1, 0, -871479596, -10780801234896]\) | \(-11845731628994222232016/1269935194601506875\) | \(-7847205986616908723017440000\) | \([2]\) | \(291962880\) | \(4.0909\) |
Rank
sage: E.rank()
The elliptic curves in class 450840.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.bx do not have complex multiplication.Modular form 450840.2.a.bx
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.
