Properties

Label 177450.bs
Number of curves $3$
Conductor $177450$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: 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)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{11} - q^{12} - q^{14} + q^{16} + 3 q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.