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Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 56550.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.i1 56550l2 \([1, 1, 0, -2412950, 942556500]\) \(795497689530094517/263435341962624\) \(514522152270750000000\) \([2]\) \(3655680\) \(2.6770\)  
56550.i2 56550l1 \([1, 1, 0, -2172950, 1231756500]\) \(580955924718082997/122133233664\) \(238541472000000000\) \([2]\) \(1827840\) \(2.3304\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 56550.2.a.i

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