Properties

Label 182070.l
Number of curves $8$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("182070.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.l1 182070dj8 [1, -1, 0, -16779105, -16639338425] [2] 21233664  
182070.l2 182070dj5 [1, -1, 0, -14984415, -22322091659] [2] 7077888  
182070.l3 182070dj6 [1, -1, 0, -7025355, 6978391825] [2, 2] 10616832  
182070.l4 182070dj3 [1, -1, 0, -6973335, 7089496141] [2] 5308416  
182070.l5 182070dj2 [1, -1, 0, -939015, -346658819] [2, 2] 3538944  
182070.l6 182070dj4 [1, -1, 0, -210735, -871166075] [2] 7077888  
182070.l7 182070dj1 [1, -1, 0, -106695, 4746685] [2] 1769472 \(\Gamma_0(N)\)-optimal
182070.l8 182070dj7 [1, -1, 0, 1896075, 23484821611] [2] 21233664  

Rank

sage: E.rank()
 

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

Modular form 182070.2.a.l

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.