Properties

Label 55473.n
Number of curves $4$
Conductor $55473$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 55473.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55473.n1 55473l4 \([1, 0, 1, -246302, 46982081]\) \(347873904937/395307\) \(1877749457196987\) \([2]\) \(422400\) \(1.8442\)  
55473.n2 55473l2 \([1, 0, 1, -19367, 324245]\) \(169112377/88209\) \(419001944994369\) \([2, 2]\) \(211200\) \(1.4976\)  
55473.n3 55473l1 \([1, 0, 1, -10962, -438929]\) \(30664297/297\) \(1410780959577\) \([2]\) \(105600\) \(1.1510\) \(\Gamma_0(N)\)-optimal
55473.n4 55473l3 \([1, 0, 1, 73088, 2543165]\) \(9090072503/5845851\) \(-27768401627354091\) \([2]\) \(422400\) \(1.8442\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 55473.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.