Properties

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

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Show commands: SageMath
E = EllipticCurve("nw1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.nw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.nw1 176400fx1 \([0, 0, 0, -54075, -1849750]\) \(1092727/540\) \(8641624320000000\) \([2]\) \(884736\) \(1.7510\) \(\Gamma_0(N)\)-optimal
176400.nw2 176400fx2 \([0, 0, 0, 197925, -14197750]\) \(53582633/36450\) \(-583309641600000000\) \([2]\) \(1769472\) \(2.0976\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400.nw have rank \(2\).

Complex multiplication

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

Modular form 176400.2.a.nw

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} - 2 q^{13} - 4 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.