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Properties

Label 56550r
Number of curves $2$
Conductor $56550$
CM no
Rank $0$
Graph

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

Elliptic curves in class 56550r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.r1 56550r1 \([1, 0, 1, -242276, -15014302]\) \(100654290922421809/52033093632000\) \(813017088000000000\) \([2]\) \(921600\) \(2.1287\) \(\Gamma_0(N)\)-optimal
56550.r2 56550r2 \([1, 0, 1, 909724, -116390302]\) \(5328847957372469711/3458851344000000\) \(-54044552250000000000\) \([2]\) \(1843200\) \(2.4752\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56550r have rank \(0\).

Complex multiplication

The elliptic curves in class 56550r do not have complex multiplication.

Modular form 56550.2.a.r

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.