Properties

Label 5775.g
Number of curves $4$
Conductor $5775$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5775.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5775.g1 5775o3 \([1, 0, 0, -517563, -40647258]\) \(981281029968144361/522287841796875\) \(8160747528076171875\) \([2]\) \(110592\) \(2.3202\)  
5775.g2 5775o2 \([1, 0, 0, -406188, -99564633]\) \(474334834335054841/607815140625\) \(9497111572265625\) \([2, 2]\) \(55296\) \(1.9736\)  
5775.g3 5775o1 \([1, 0, 0, -406063, -99629008]\) \(473897054735271721/779625\) \(12181640625\) \([2]\) \(27648\) \(1.6270\) \(\Gamma_0(N)\)-optimal
5775.g4 5775o4 \([1, 0, 0, -296813, -154361508]\) \(-185077034913624841/551466161890875\) \(-8616658779544921875\) \([2]\) \(110592\) \(2.3202\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5775.g have rank \(0\).

Complex multiplication

The elliptic curves in class 5775.g do not have complex multiplication.

Modular form 5775.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.