Properties

Label 235200.nw
Number of curves $2$
Conductor $235200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 235200.nw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.nw1 235200nw2 \([0, -1, 0, -229640833, -1339358890463]\) \(266916252066900625/162\) \(812851200000000\) \([]\) \(24883200\) \(3.0836\)  
235200.nw2 235200nw1 \([0, -1, 0, -2840833, -1828570463]\) \(505318200625/4251528\) \(21332466892800000000\) \([]\) \(8294400\) \(2.5343\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235200.nw have rank \(0\).

Complex multiplication

The elliptic curves in class 235200.nw do not have complex multiplication.

Modular form 235200.2.a.nw

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 6 q^{11} - 4 q^{13} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.