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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 53550bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53550.p3 | 53550bb1 | \([1, -1, 0, -11540817, -15087450659]\) | \(14924020698027934921/161083883520\) | \(1834846110720000000\) | \([2]\) | \(2949120\) | \(2.6596\) | \(\Gamma_0(N)\)-optimal |
| 53550.p2 | 53550bb2 | \([1, -1, 0, -11828817, -14294586659]\) | \(16069416876629693641/1546622367494400\) | \(17616995404740900000000\) | \([2, 2]\) | \(5898240\) | \(3.0061\) | |
| 53550.p4 | 53550bb3 | \([1, -1, 0, 14181183, -68421396659]\) | \(27689398696638536759/193555307298039120\) | \(-2204715922191726851250000\) | \([2]\) | \(11796480\) | \(3.3527\) | |
| 53550.p1 | 53550bb4 | \([1, -1, 0, -42446817, 90572063341]\) | \(742525803457216841161/118657634071410000\) | \(1351584613094654531250000\) | \([2]\) | \(11796480\) | \(3.3527\) |
Rank
sage: E.rank()
The elliptic curves in class 53550bb have rank \(1\).
Complex multiplication
The elliptic curves in class 53550bb do not have complex multiplication.Modular form 53550.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
