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Properties

Label 2550.l
Number of curves $8$
Conductor $2550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 2550.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.l1 2550h7 \([1, 0, 1, -2836751, -1839219352]\) \(161572377633716256481/914742821250\) \(14292856582031250\) \([2]\) \(49152\) \(2.2915\)  
2550.l2 2550h4 \([1, 0, 1, -544001, 154390148]\) \(1139466686381936641/4080\) \(63750000\) \([2]\) \(12288\) \(1.5983\)  
2550.l3 2550h5 \([1, 0, 1, -180501, -27656852]\) \(41623544884956481/2962701562500\) \(46292211914062500\) \([2, 2]\) \(24576\) \(1.9449\)  
2550.l4 2550h3 \([1, 0, 1, -36001, 2110148]\) \(330240275458561/67652010000\) \(1057062656250000\) \([2, 2]\) \(12288\) \(1.5983\)  
2550.l5 2550h2 \([1, 0, 1, -34001, 2410148]\) \(278202094583041/16646400\) \(260100000000\) \([2, 2]\) \(6144\) \(1.2517\)  
2550.l6 2550h1 \([1, 0, 1, -2001, 42148]\) \(-56667352321/16711680\) \(-261120000000\) \([2]\) \(3072\) \(0.90516\) \(\Gamma_0(N)\)-optimal
2550.l7 2550h6 \([1, 0, 1, 76499, 12685148]\) \(3168685387909439/6278181696900\) \(-98096589014062500\) \([2]\) \(24576\) \(1.9449\)  
2550.l8 2550h8 \([1, 0, 1, 163749, -120604352]\) \(31077313442863199/420227050781250\) \(-6566047668457031250\) \([2]\) \(49152\) \(2.2915\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2550.l have rank \(0\).

Complex multiplication

The elliptic curves in class 2550.l do not have complex multiplication.

Modular form 2550.2.a.l

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

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.