Properties

Label 182070v
Number of curves 8
Conductor 182070
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("182070.df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.df7 182070v1 [1, -1, 1, -1294052, -566057721] [2] 3538944 \(\Gamma_0(N)\)-optimal
182070.df6 182070v2 [1, -1, 1, -1502132, -371627769] [2, 2] 7077888  
182070.df5 182070v3 [1, -1, 1, -3830027, 2193551259] [2] 10616832  
182070.df4 182070v4 [1, -1, 1, -11333912, 14431100199] [2] 14155776  
182070.df8 182070v5 [1, -1, 1, 5000368, -2733335769] [2] 14155776  
182070.df2 182070v6 [1, -1, 1, -57098507, 166068703131] [2, 2] 21233664  
182070.df1 182070v7 [1, -1, 1, -913555787, 10628208252699] [2] 42467328  
182070.df3 182070v8 [1, -1, 1, -52936907, 191299651611] [2] 42467328  

Rank

sage: E.rank()
 

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

Modular form 182070.2.a.df

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.