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Properties

Label 177450io
Number of curves $2$
Conductor $177450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("io1")
 
E.isogeny_class()
 

Elliptic curves in class 177450io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bb1 177450io1 \([1, 1, 0, -720450, 233806500]\) \(4386781853/27216\) \(256575065906250000\) \([2]\) \(3686400\) \(2.1785\) \(\Gamma_0(N)\)-optimal
177450.bb2 177450io2 \([1, 1, 0, -297950, 506319000]\) \(-310288733/11573604\) \(-109108546776632812500\) \([2]\) \(7372800\) \(2.5251\)  

Rank

sage: E.rank()
 

The elliptic curves in class 177450io have rank \(0\).

Complex multiplication

The elliptic curves in class 177450io do not have complex multiplication.

Modular form 177450.2.a.io

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 2 q^{11} - q^{12} + q^{14} + q^{16} + 8 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.