Properties

Label 35490.a
Number of curves $6$
Conductor $35490$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35490.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35490.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35490.a1 35490b6 [1, 1, 0, -2839203, -1842560793] [2] 589824  
35490.a2 35490b4 [1, 1, 0, -177453, -28844343] [2, 2] 294912  
35490.a3 35490b5 [1, 1, 0, -165623, -32840517] [2] 589824  
35490.a4 35490b3 [1, 1, 0, -62533, 5662753] [2] 294912  
35490.a5 35490b2 [1, 1, 0, -11833, -390827] [2, 2] 147456  
35490.a6 35490b1 [1, 1, 0, 1687, -36603] [2] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 35490.2.a.a

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.