Properties

Label 55506.w
Number of curves $2$
Conductor $55506$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 55506.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.w1 55506s2 \([1, 0, 1, -24150174, -45339549296]\) \(2618764779527817409/22654590064128\) \(13475478497838219929088\) \([2]\) \(8467200\) \(3.0706\)  
55506.w2 55506s1 \([1, 0, 1, -467614, -1668908656]\) \(-19010647320769/2011741028352\) \(-1196630479476291796992\) \([2]\) \(4233600\) \(2.7240\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55506.w have rank \(1\).

Complex multiplication

The elliptic curves in class 55506.w do not have complex multiplication.

Modular form 55506.2.a.w

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