Properties

Label 5550m
Number of curves $6$
Conductor $5550$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5550.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5550m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5550.r5 5550m1 [1, 0, 1, -21126, 4066648] [2] 41472 \(\Gamma_0(N)\)-optimal
5550.r4 5550m2 [1, 0, 1, -533126, 149474648] [2, 2] 82944  
5550.r3 5550m3 [1, 0, 1, -733126, 27074648] [2, 2] 165888  
5550.r1 5550m4 [1, 0, 1, -8525126, 9580034648] [2] 165888  
5550.r2 5550m5 [1, 0, 1, -7578126, -7995265352] [2] 331776  
5550.r6 5550m6 [1, 0, 1, 2911874, 216614648] [2] 331776  

Rank

sage: E.rank()
 

The elliptic curves in class 5550m have rank \(0\).

Modular form 5550.2.a.r

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.