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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 178752.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178752.bk1 | 178752ir4 | \([0, -1, 0, -116193569, -482043575775]\) | \(22501000029889239268/3620708343\) | \(27916547905657700352\) | \([2]\) | \(18874368\) | \(3.1337\) | |
| 178752.bk2 | 178752ir2 | \([0, -1, 0, -7284209, -7481930511]\) | \(22174957026242512/278654127129\) | \(537122888132193828864\) | \([2, 2]\) | \(9437184\) | \(2.7871\) | |
| 178752.bk3 | 178752ir3 | \([0, -1, 0, -1251329, -19505460351]\) | \(-28104147578308/21301741002339\) | \(-164241639157542486736896\) | \([2]\) | \(18874368\) | \(3.1337\) | |
| 178752.bk4 | 178752ir1 | \([0, -1, 0, -854429, 119355405]\) | \(572616640141312/280535480757\) | \(33796832026194220032\) | \([2]\) | \(4718592\) | \(2.4405\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 178752.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 178752.bk do not have complex multiplication.Modular form 178752.2.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 LMFDB 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 LMFDB labels.
