Properties

Label 35490bh
Number of curves 8
Conductor 35490
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35490.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35490bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35490.bj7 35490bh1 [1, 0, 1, 35486, 1941812] [2] 294912 \(\Gamma_0(N)\)-optimal
35490.bj6 35490bh2 [1, 0, 1, -180834, 17343796] [2, 2] 589824  
35490.bj5 35490bh3 [1, 0, 1, -1275954, -542481548] [2, 2] 1179648  
35490.bj4 35490bh4 [1, 0, 1, -2546834, 1563761396] [2] 1179648  
35490.bj8 35490bh5 [1, 0, 1, 214626, -1733753084] [2] 2359296  
35490.bj2 35490bh6 [1, 0, 1, -20288454, -35175651548] [2, 2] 2359296  
35490.bj3 35490bh7 [1, 0, 1, -20161704, -35636818748] [2] 4718592  
35490.bj1 35490bh8 [1, 0, 1, -324615204, -2251161314348] [2] 4718592  

Rank

sage: E.rank()
 

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

Modular form 35490.2.a.bj

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} - q^{14} - q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.