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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 80850bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80850.cj4 | 80850bx1 | \([1, 0, 1, 94299, -6619952]\) | \(50447927375/39517632\) | \(-72643904487000000\) | \([2]\) | \(663552\) | \(1.9234\) | \(\Gamma_0(N)\)-optimal |
| 80850.cj3 | 80850bx2 | \([1, 0, 1, -444701, -57285952]\) | \(5290763640625/2291573592\) | \(4212520961331375000\) | \([2]\) | \(1327104\) | \(2.2699\) | |
| 80850.cj2 | 80850bx3 | \([1, 0, 1, -1008201, 494797048]\) | \(-61653281712625/21875235228\) | \(-40212492958421437500\) | \([2]\) | \(1990656\) | \(2.4727\) | |
| 80850.cj1 | 80850bx4 | \([1, 0, 1, -17312951, 27723729548]\) | \(312196988566716625/25367712678\) | \(46632594200844093750\) | \([2]\) | \(3981312\) | \(2.8192\) |
Rank
sage: E.rank()
The elliptic curves in class 80850bx have rank \(1\).
Complex multiplication
The elliptic curves in class 80850bx do not have complex multiplication.Modular form 80850.2.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.
