Properties

Label 182070.cw
Number of curves $2$
Conductor $182070$
CM no
Rank $0$
Graph

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

Elliptic curves in class 182070.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.cw1 182070be2 \([1, -1, 1, -98014838, 373055777381]\) \(5918043195362419129/8515734343200\) \(149845312339806907303200\) \([2]\) \(35389440\) \(3.3494\)  
182070.cw2 182070be1 \([1, -1, 1, -4378838, 9223735781]\) \(-527690404915129/1782829440000\) \(-31371179926335661440000\) \([2]\) \(17694720\) \(3.0028\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 182070.cw have rank \(0\).

Complex multiplication

The elliptic curves in class 182070.cw do not have complex multiplication.

Modular form 182070.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + 2 q^{11} + 4 q^{13} + q^{14} + q^{16} - 6 q^{19} + O(q^{20})\) 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.