Properties

Label 2550k
Number of curves $4$
Conductor $2550$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 2550k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.n3 2550k1 \([1, 0, 1, -2526, 42448]\) \(114013572049/15667200\) \(244800000000\) \([2]\) \(4608\) \(0.91210\) \(\Gamma_0(N)\)-optimal
2550.n2 2550k2 \([1, 0, 1, -10526, -373552]\) \(8253429989329/936360000\) \(14630625000000\) \([2, 2]\) \(9216\) \(1.2587\)  
2550.n1 2550k3 \([1, 0, 1, -163526, -25465552]\) \(30949975477232209/478125000\) \(7470703125000\) \([2]\) \(18432\) \(1.6053\)  
2550.n4 2550k4 \([1, 0, 1, 14474, -1873552]\) \(21464092074671/109596256200\) \(-1712441503125000\) \([2]\) \(18432\) \(1.6053\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2550.2.a.k

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