Properties

Label 176400.qy
Number of curves $2$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("qy1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.qy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.qy1 176400gm2 \([0, 0, 0, -86616075, 310286632250]\) \(-5452947409/250\) \(-3294791304336000000000\) \([]\) \(17418240\) \(3.2045\)  
176400.qy2 176400gm1 \([0, 0, 0, -180075, 1105060250]\) \(-49/40\) \(-527166608693760000000\) \([]\) \(5806080\) \(2.6552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 176400.qy have rank \(0\).

Complex multiplication

The elliptic curves in class 176400.qy do not have complex multiplication.

Modular form 176400.2.a.qy

sage: E.q_eigenform(10)
 
\(q + 3 q^{11} + 5 q^{13} - 6 q^{17} - q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.