Properties

Label 5010e
Number of curves $4$
Conductor $5010$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 5010e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5010.e3 5010e1 \([1, 1, 1, -471, -4131]\) \(11556972012529/360720\) \(360720\) \([2]\) \(1824\) \(0.16274\) \(\Gamma_0(N)\)-optimal
5010.e2 5010e2 \([1, 1, 1, -491, -3787]\) \(13092526729009/2033108100\) \(2033108100\) \([2, 2]\) \(3648\) \(0.50931\)  
5010.e1 5010e3 \([1, 1, 1, -2161, 34289]\) \(1116093485689489/110938308750\) \(110938308750\) \([2]\) \(7296\) \(0.85589\)  
5010.e4 5010e4 \([1, 1, 1, 859, -19447]\) \(70092508729391/210005006670\) \(-210005006670\) \([2]\) \(7296\) \(0.85589\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5010e have rank \(0\).

Complex multiplication

The elliptic curves in class 5010e do not have complex multiplication.

Modular form 5010.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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 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.