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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 11200.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11200.bt1 | 11200p3 | \([0, 0, 0, -428300, -107882000]\) | \(2121328796049/120050\) | \(491724800000000\) | \([2]\) | \(73728\) | \(1.8834\) | |
| 11200.bt2 | 11200p4 | \([0, 0, 0, -140300, 18902000]\) | \(74565301329/5468750\) | \(22400000000000000\) | \([2]\) | \(73728\) | \(1.8834\) | |
| 11200.bt3 | 11200p2 | \([0, 0, 0, -28300, -1482000]\) | \(611960049/122500\) | \(501760000000000\) | \([2, 2]\) | \(36864\) | \(1.5369\) | |
| 11200.bt4 | 11200p1 | \([0, 0, 0, 3700, -138000]\) | \(1367631/2800\) | \(-11468800000000\) | \([2]\) | \(18432\) | \(1.1903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 11200.bt do not have complex multiplication.Modular form 11200.2.a.bt
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.
