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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 38640bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bc2 | 38640bx1 | \([0, -1, 0, -25800, -1586448]\) | \(463702796512201/15214500\) | \(62318592000\) | \([2]\) | \(69120\) | \(1.1650\) | \(\Gamma_0(N)\)-optimal |
| 38640.bc3 | 38640bx2 | \([0, -1, 0, -24680, -1731600]\) | \(-405897921250921/84358968750\) | \(-345534336000000\) | \([2]\) | \(138240\) | \(1.5116\) | |
| 38640.bc1 | 38640bx3 | \([0, -1, 0, -46200, 1272432]\) | \(2662558086295801/1374177967680\) | \(5628632955617280\) | \([2]\) | \(207360\) | \(1.7143\) | |
| 38640.bc4 | 38640bx4 | \([0, -1, 0, 173320, 9702000]\) | \(140574743422291079/91397357868600\) | \(-374363577829785600\) | \([2]\) | \(414720\) | \(2.0609\) |
Rank
sage: E.rank()
The elliptic curves in class 38640bx have rank \(0\).
Complex multiplication
The elliptic curves in class 38640bx do not have complex multiplication.Modular form 38640.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
