Properties

Label 55473.o
Number of curves $2$
Conductor $55473$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 55473.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55473.o1 55473k1 \([1, 0, 1, -917, 10595]\) \(1235376017/1089\) \(75054969\) \([2]\) \(26880\) \(0.43654\) \(\Gamma_0(N)\)-optimal
55473.o2 55473k2 \([1, 0, 1, -712, 15515]\) \(-578009537/1185921\) \(-81734861241\) \([2]\) \(53760\) \(0.78311\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55473.o have rank \(0\).

Complex multiplication

The elliptic curves in class 55473.o do not have complex multiplication.

Modular form 55473.2.a.o

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