Properties

Label 182070du
Number of curves $4$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("182070.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.be2 182070du1 [1, -1, 0, -30399, 2045113] [2] 497664 \(\Gamma_0(N)\)-optimal
182070.be3 182070du2 [1, -1, 0, -21729, 3229435] [2] 995328  
182070.be1 182070du3 [1, -1, 0, -121434, -14242060] [2] 1492992  
182070.be4 182070du4 [1, -1, 0, 190686, -75604852] [2] 2985984  

Rank

sage: E.rank()
 

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

Modular form 182070.2.a.be

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.