Properties

Label 101761.e
Number of curves $2$
Conductor $101761$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 101761.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101761.e1 101761c2 [1, 0, 0, -3054950, 2055018109] [] 1513512  
101761.e2 101761c1 [1, 0, 0, -2120, -147047] [] 137592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101761.e have rank \(0\).

Complex multiplication

The elliptic curves in class 101761.e do not have complex multiplication.

Modular form 101761.2.a.e

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

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.