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Properties

Label 55470.u
Number of curves $2$
Conductor $55470$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 55470.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55470.u1 55470s2 \([1, 1, 1, -439176, 108261153]\) \(1481933914201/53916840\) \(340827920094845160\) \([2]\) \(1064448\) \(2.1339\)  
55470.u2 55470s1 \([1, 1, 1, -69376, -4749727]\) \(5841725401/1857600\) \(11742563999822400\) \([2]\) \(532224\) \(1.7873\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55470.u have rank \(1\).

Complex multiplication

The elliptic curves in class 55470.u do not have complex multiplication.

Modular form 55470.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} - q^{12} - 2 q^{13} + 2 q^{14} + q^{15} + q^{16} - 4 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 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.