Properties

Label 177450ki
Number of curves $4$
Conductor $177450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ki1")
 
E.isogeny_class()
 

Elliptic curves in class 177450ki

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bl3 177450ki1 \([1, 1, 0, -238800, -43776000]\) \(19968681097/628992\) \(47437878852000000\) \([2]\) \(2064384\) \(1.9747\) \(\Gamma_0(N)\)-optimal
177450.bl2 177450ki2 \([1, 1, 0, -576800, 107310000]\) \(281397674377/96589584\) \(7284679271210250000\) \([2, 2]\) \(4128768\) \(2.3213\)  
177450.bl1 177450ki3 \([1, 1, 0, -8266300, 9142472500]\) \(828279937799497/193444524\) \(14589371397561187500\) \([2]\) \(8257536\) \(2.6678\)  
177450.bl4 177450ki4 \([1, 1, 0, 1704700, 748411500]\) \(7264187703863/7406095788\) \(-558559528193445187500\) \([2]\) \(8257536\) \(2.6678\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.ki

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.