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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 11200.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.bq1 | 11200bu4 | \([0, 0, 0, -428300, 107882000]\) | \(2121328796049/120050\) | \(491724800000000\) | \([2]\) | \(73728\) | \(1.8834\) | |
11200.bq2 | 11200bu3 | \([0, 0, 0, -140300, -18902000]\) | \(74565301329/5468750\) | \(22400000000000000\) | \([2]\) | \(73728\) | \(1.8834\) | |
11200.bq3 | 11200bu2 | \([0, 0, 0, -28300, 1482000]\) | \(611960049/122500\) | \(501760000000000\) | \([2, 2]\) | \(36864\) | \(1.5369\) | |
11200.bq4 | 11200bu1 | \([0, 0, 0, 3700, 138000]\) | \(1367631/2800\) | \(-11468800000000\) | \([2]\) | \(18432\) | \(1.1903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 11200.bq do not have complex multiplication.Modular form 11200.2.a.bq
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.