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Properties

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

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Show commands: SageMath
E = EllipticCurve("ke1")
 
E.isogeny_class()
 

Elliptic curves in class 177450ke

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bh2 177450ke1 \([1, 1, 0, -16918125, -26838984375]\) \(-15600206875151814733/32299804687500\) \(-1108791732788085937500\) \([2]\) \(17418240\) \(2.9241\) \(\Gamma_0(N)\)-optimal
177450.bh1 177450ke2 \([1, 1, 0, -270824375, -1715569453125]\) \(63993649810037164314733/273488906250\) \(9388361359863281250\) \([2]\) \(34836480\) \(3.2706\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.ke

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