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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 19350.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19350.bx1 | 19350by2 | \([1, -1, 1, -13477730, 19050287397]\) | \(-23769846831649063249/3261823333284\) | \(-37154206405688062500\) | \([]\) | \(1317120\) | \(2.7729\) | |
| 19350.bx2 | 19350by1 | \([1, -1, 1, 35770, -5826603]\) | \(444369620591/1540767744\) | \(-17550307584000000\) | \([]\) | \(188160\) | \(1.8000\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19350.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 19350.bx do not have complex multiplication.Modular form 19350.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
