Properties

Label 850.e
Number of curves 4
Conductor 850
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("850.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 850.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
850.e1 850b4 [1, 1, 0, -2825, -41125] [2] 1728  
850.e2 850b3 [1, 1, 0, -2575, -51375] [2] 864  
850.e3 850b2 [1, 1, 0, -1075, 13125] [2] 576  
850.e4 850b1 [1, 1, 0, -75, 125] [2] 288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 850.e have rank \(0\).

Modular form 850.2.a.e

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.