Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("iq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177450iq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bm2 177450iq1 \([1, 1, 0, 103425, -997875]\) \(2595575/1512\) \(-71270851640625000\) \([]\) \(2527200\) \(1.9232\) \(\Gamma_0(N)\)-optimal
177450.bm1 177450iq2 \([1, 1, 0, -1480950, -734563500]\) \(-7620530425/526848\) \(-24833932305000000000\) \([]\) \(7581600\) \(2.4725\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.iq

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