Properties

Label 189630.di
Number of curves $4$
Conductor $189630$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("di1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189630.di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189630.di1 189630bg3 [1, -1, 1, -369788, 86054217] [2] 1769472  
189630.di2 189630bg2 [1, -1, 1, -39038, -734583] [2, 2] 884736  
189630.di3 189630bg1 [1, -1, 1, -30218, -2011719] [2] 442368 \(\Gamma_0(N)\)-optimal
189630.di4 189630bg4 [1, -1, 1, 150592, -5892519] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 189630.di have rank \(0\).

Complex multiplication

The elliptic curves in class 189630.di do not have complex multiplication.

Modular form 189630.2.a.di

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{13} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.