Properties

Label 90354.c
Number of curves 4
Conductor 90354
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("90354.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 90354.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
90354.c1 90354a4 [1, 1, 0, -481916, -128968170] [2] 811008  
90354.c2 90354a2 [1, 1, 0, -30146, -2020800] [2, 2] 405504  
90354.c3 90354a3 [1, 1, 0, -16456, -3847046] [2] 811008  
90354.c4 90354a1 [1, 1, 0, -2766, -156] [2] 202752 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90354.c have rank \(1\).

Modular form 90354.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} + 2q^{10} - q^{11} - q^{12} + 6q^{13} + 4q^{14} + 2q^{15} + q^{16} - 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.