Properties

Label 5355q
Number of curves 4
Conductor 5355
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5355.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5355q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5355.r4 5355q1 [1, -1, 0, 126, -945] [2] 2048 \(\Gamma_0(N)\)-optimal
5355.r3 5355q2 [1, -1, 0, -999, -9720] [2, 2] 4096  
5355.r1 5355q3 [1, -1, 0, -15174, -715635] [2] 8192  
5355.r2 5355q4 [1, -1, 0, -4824, 121095] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 5355q have rank \(1\).

Modular form 5355.2.a.r

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.