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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 101430.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.bx1 | 101430bz1 | \([1, -1, 0, -2277774, -1321648812]\) | \(15238420194810961/12619514880\) | \(1082326840159380480\) | \([2]\) | \(2580480\) | \(2.3888\) | \(\Gamma_0(N)\)-optimal |
| 101430.bx2 | 101430bz2 | \([1, -1, 0, -1783854, -1911092940]\) | \(-7319577278195281/14169067365600\) | \(-1215225946135200837600\) | \([2]\) | \(5160960\) | \(2.7354\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.bx do not have complex multiplication.Modular form 101430.2.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.
