Properties

Label 35490ct
Number of curves $4$
Conductor $35490$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35490ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35490.cw3 35490ct1 [1, 1, 1, -595, -3775] [2] 36864 \(\Gamma_0(N)\)-optimal
35490.cw2 35490ct2 [1, 1, 1, -3975, 92217] [2, 2] 73728  
35490.cw4 35490ct3 [1, 1, 1, 1095, 317325] [2] 147456  
35490.cw1 35490ct4 [1, 1, 1, -63125, 6078197] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 35490ct have rank \(0\).

Complex multiplication

The elliptic curves in class 35490ct do not have complex multiplication.

Modular form 35490.2.a.ct

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.