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SageMath
sage: E = EllipticCurve("bk1")
sage: E.isogeny_class()
Elliptic curves in class 11200.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11200.bk1 | 11200bv3 | \([0, 0, 0, -29900, -1990000]\) | \(1443468546/7\) | \(14336000000\) | \([2]\) | \(16384\) | \(1.1493\) | |
| 11200.bk2 | 11200bv4 | \([0, 0, 0, -5900, 138000]\) | \(11090466/2401\) | \(4917248000000\) | \([2]\) | \(16384\) | \(1.1493\) | |
| 11200.bk3 | 11200bv2 | \([0, 0, 0, -1900, -30000]\) | \(740772/49\) | \(50176000000\) | \([2, 2]\) | \(8192\) | \(0.80269\) | |
| 11200.bk4 | 11200bv1 | \([0, 0, 0, 100, -2000]\) | \(432/7\) | \(-1792000000\) | \([2]\) | \(4096\) | \(0.45611\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 11200.bk do not have complex multiplication.Modular form 11200.2.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.
