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Properties

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

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Show commands: SageMath
E = EllipticCurve("kb1")
 
E.isogeny_class()
 

Elliptic curves in class 177450kb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bd2 177450kb1 \([1, 1, 0, -2200, -5000]\) \(2640625/1512\) \(674753625000\) \([]\) \(290304\) \(0.95951\) \(\Gamma_0(N)\)-optimal
177450.bd1 177450kb2 \([1, 1, 0, -128950, -17876750]\) \(531373116625/2058\) \(918414656250\) \([]\) \(870912\) \(1.5088\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.kb

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} + q^{14} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.