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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 41616bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41616.bu2 | 41616bx1 | \([0, 0, 0, -10633755, 13341870538]\) | \(1845026709625/793152\) | \(57165950410501128192\) | \([2]\) | \(1327104\) | \(2.7512\) | \(\Gamma_0(N)\)-optimal |
| 41616.bu3 | 41616bx2 | \([0, 0, 0, -8969115, 17660279626]\) | \(-1107111813625/1228691592\) | \(-88557202929667560210432\) | \([2]\) | \(2654208\) | \(3.0978\) | |
| 41616.bu1 | 41616bx3 | \([0, 0, 0, -31233675, -50795418566]\) | \(46753267515625/11591221248\) | \(835430256823805524574208\) | \([2]\) | \(3981312\) | \(3.3005\) | |
| 41616.bu4 | 41616bx4 | \([0, 0, 0, 75303285, -322102440902]\) | \(655215969476375/1001033261568\) | \(-72148866535113689218940928\) | \([2]\) | \(7962624\) | \(3.6471\) |
Rank
sage: E.rank()
The elliptic curves in class 41616bx have rank \(1\).
Complex multiplication
The elliptic curves in class 41616bx do not have complex multiplication.Modular form 41616.2.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.
