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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 423864.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 423864.bx1 | 423864bx1 | \([0, 0, 0, -45414, -3292515]\) | \(55296/7\) | \(1311285631851216\) | \([2]\) | \(2247168\) | \(1.6300\) | \(\Gamma_0(N)\)-optimal |
| 423864.bx2 | 423864bx2 | \([0, 0, 0, 68121, -17121078]\) | \(11664/49\) | \(-146863990767336192\) | \([2]\) | \(4494336\) | \(1.9766\) |
Rank
sage: E.rank()
The elliptic curves in class 423864.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 423864.bx do not have complex multiplication.Modular form 423864.2.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.
