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Properties

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

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Show commands: SageMath
E = EllipticCurve("jw1")
 
E.isogeny_class()
 

Elliptic curves in class 177450jw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.r2 177450jw1 \([1, 1, 0, -1937250, 1109902500]\) \(-4852559557/408240\) \(-67643450375523750000\) \([2]\) \(6469632\) \(2.5502\) \(\Gamma_0(N)\)-optimal
177450.r1 177450jw2 \([1, 1, 0, -31596750, 68347989000]\) \(21054298635397/132300\) \(21921488547623437500\) \([2]\) \(12939264\) \(2.8968\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.jw

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