Properties

Label 177450ka
Number of curves $2$
Conductor $177450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ka1")
 
E.isogeny_class()
 

Elliptic curves in class 177450ka

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bc2 177450ka1 \([1, 1, 0, -5649891900, -163556553438000]\) \(-44694151057272491356949809/30197762286189281280\) \(-13476223260247688478720000000\) \([]\) \(239500800\) \(4.3357\) \(\Gamma_0(N)\)-optimal
177450.bc1 177450ka2 \([1, 1, 0, -457715427900, -119190635459550000]\) \(-23763856998804796987128199384369/7318708992000\) \(-3266088242508000000000\) \([]\) \(718502400\) \(4.8850\)  

Rank

sage: E.rank()
 

The elliptic curves in class 177450ka have rank \(1\).

Complex multiplication

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

Modular form 177450.2.a.ka

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.