Properties

Label 56550.g
Number of curves $4$
Conductor $56550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 56550.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.g1 56550i4 \([1, 1, 0, -104414875, -410712246875]\) \(8057323694463985606146481/638717154543000\) \(9979955539734375000\) \([2]\) \(6635520\) \(3.0915\)  
56550.g2 56550i2 \([1, 1, 0, -6539875, -6390621875]\) \(1979758117698975186481/17510434929000000\) \(273600545765625000000\) \([2, 2]\) \(3317760\) \(2.7449\)  
56550.g3 56550i3 \([1, 1, 0, -1976875, -15137892875]\) \(-54681655838565466801/6303365630859375000\) \(-98490087982177734375000\) \([2]\) \(6635520\) \(3.0915\)  
56550.g4 56550i1 \([1, 1, 0, -707875, 65402125]\) \(2510581756496128561/1333551278592000\) \(20836738728000000000\) \([2]\) \(1658880\) \(2.3984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 56550.g have rank \(1\).

Complex multiplication

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

Modular form 56550.2.a.g

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