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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 29232bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.t2 | 29232bk1 | \([0, 0, 0, -29235, -5837582]\) | \(-925434168625/4394621952\) | \(-13122270834720768\) | \([2]\) | \(184320\) | \(1.7774\) | \(\Gamma_0(N)\)-optimal |
| 29232.t1 | 29232bk2 | \([0, 0, 0, -697395, -223791374]\) | \(12562403073144625/24165685152\) | \(72158349212909568\) | \([2]\) | \(368640\) | \(2.1239\) |
Rank
sage: E.rank()
The elliptic curves in class 29232bk have rank \(0\).
Complex multiplication
The elliptic curves in class 29232bk do not have complex multiplication.Modular form 29232.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
