Properties

Label 190440.bw
Number of curves $4$
Conductor $190440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 190440.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190440.bw1 190440g4 \([0, 0, 0, -509427, -139944834]\) \(132304644/5\) \(552540994974720\) \([2]\) \(1576960\) \(1.9148\)  
190440.bw2 190440g2 \([0, 0, 0, -33327, -1971054]\) \(148176/25\) \(690676243718400\) \([2, 2]\) \(788480\) \(1.5683\)  
190440.bw3 190440g1 \([0, 0, 0, -9522, 328509]\) \(55296/5\) \(8633453046480\) \([2]\) \(394240\) \(1.2217\) \(\Gamma_0(N)\)-optimal
190440.bw4 190440g3 \([0, 0, 0, 61893, -11169306]\) \(237276/625\) \(-69067624371840000\) \([2]\) \(1576960\) \(1.9148\)  

Rank

sage: E.rank()
 

The elliptic curves in class 190440.bw have rank \(1\).

Complex multiplication

The elliptic curves in class 190440.bw do not have complex multiplication.

Modular form 190440.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.