Properties

Label 35490.bo
Number of curves $8$
Conductor $35490$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("35490.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35490.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35490.bo1 35490bm8 [1, 0, 1, -1090223, 275563628] [2] 1327104  
35490.bo2 35490bm5 [1, 0, 1, -973613, 369685136] [2] 442368  
35490.bo3 35490bm6 [1, 0, 1, -456473, -115586872] [2, 2] 663552  
35490.bo4 35490bm3 [1, 0, 1, -453093, -117426944] [2] 331776  
35490.bo5 35490bm2 [1, 0, 1, -61013, 5740256] [2, 2] 221184  
35490.bo6 35490bm4 [1, 0, 1, -13693, 14428208] [2] 442368  
35490.bo7 35490bm1 [1, 0, 1, -6933, -78752] [2] 110592 \(\Gamma_0(N)\)-optimal
35490.bo8 35490bm7 [1, 0, 1, 123197, -388959244] [2] 1327104  

Rank

sage: E.rank()
 

The elliptic curves in class 35490.bo have rank \(1\).

Modular form 35490.2.a.bo

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.