Properties

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

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Show commands: SageMath
E = EllipticCurve("gx1")
 
E.isogeny_class()
 

Elliptic curves in class 176400gx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.th2 176400gx1 \([0, 0, 0, -255675, 49396970]\) \(505318200625/4251528\) \(15551368364851200\) \([]\) \(1658880\) \(1.9324\) \(\Gamma_0(N)\)-optimal
176400.th1 176400gx2 \([0, 0, 0, -20667675, 36164756810]\) \(266916252066900625/162\) \(592568524800\) \([]\) \(4976640\) \(2.4817\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 176400.2.a.gx

sage: E.q_eigenform(10)
 
\(q + 6 q^{11} - 4 q^{13} + 3 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.