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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 17136.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17136.bk1 | 17136bl4 | \([0, 0, 0, -731379, 240747442]\) | \(14489843500598257/6246072\) | \(18650671054848\) | \([2]\) | \(147456\) | \(1.8890\) | |
| 17136.bk2 | 17136bl3 | \([0, 0, 0, -97779, -6220622]\) | \(34623662831857/14438442312\) | \(43112957728555008\) | \([2]\) | \(147456\) | \(1.8890\) | |
| 17136.bk3 | 17136bl2 | \([0, 0, 0, -45939, 3722290]\) | \(3590714269297/73410624\) | \(219202948694016\) | \([2, 2]\) | \(73728\) | \(1.5424\) | |
| 17136.bk4 | 17136bl1 | \([0, 0, 0, 141, 174130]\) | \(103823/4386816\) | \(-13098962386944\) | \([2]\) | \(36864\) | \(1.1959\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17136.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 17136.bk do not have complex multiplication.Modular form 17136.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
