Properties

Label 340704.cw
Number of curves $2$
Conductor $340704$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 340704.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
340704.cw1 340704cw2 \([0, 0, 0, -50700, -4147936]\) \(1000000/63\) \(908004790038528\) \([2]\) \(1179648\) \(1.6212\)  
340704.cw2 340704cw1 \([0, 0, 0, 2535, -272428]\) \(8000/147\) \(-33104341303488\) \([2]\) \(589824\) \(1.2747\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 340704.cw have rank \(1\).

Complex multiplication

The elliptic curves in class 340704.cw do not have complex multiplication.

Modular form 340704.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{7} - 2 q^{11} - 4 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.