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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 177450.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.bs1 | 177450iv3 | \([1, 1, 0, -110088800, -444646272000]\) | \(-1956469094246217097/36641439744\) | \(-2763456736395264000000\) | \([]\) | \(35271936\) | \(3.2387\) | |
177450.bs2 | 177450iv2 | \([1, 1, 0, -513425, -1356208875]\) | \(-198461344537/10417365504\) | \(-785666149546824000000\) | \([]\) | \(11757312\) | \(2.6893\) | |
177450.bs3 | 177450iv1 | \([1, 1, 0, 56950, 49765500]\) | \(270840023/14329224\) | \(-1080694177597125000\) | \([]\) | \(3919104\) | \(2.1400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177450.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 177450.bs do not have complex multiplication.Modular form 177450.2.a.bs
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.