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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 31680.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31680.bx1 | 31680bb1 | \([0, 0, 0, -50988, -4473808]\) | \(-76711450249/851840\) | \(-162789159075840\) | \([]\) | \(161280\) | \(1.5418\) | \(\Gamma_0(N)\)-optimal |
| 31680.bx2 | 31680bb2 | \([0, 0, 0, 170772, -23190352]\) | \(2882081488391/2883584000\) | \(-551061483945984000\) | \([]\) | \(483840\) | \(2.0911\) |
Rank
sage: E.rank()
The elliptic curves in class 31680.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 31680.bx do not have complex multiplication.Modular form 31680.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
