Properties

Label 151725.s
Number of curves $2$
Conductor $151725$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 151725.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.s1 151725bi2 \([1, 1, 1, -4324313, -2825357344]\) \(23711636464489/4590075735\) \(1731144840137315859375\) \([2]\) \(7962624\) \(2.7923\)  
151725.s2 151725bi1 \([1, 1, 1, 552562, -260121094]\) \(49471280711/106269975\) \(-40079669596730859375\) \([2]\) \(3981312\) \(2.4457\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 151725.s have rank \(1\).

Complex multiplication

The elliptic curves in class 151725.s do not have complex multiplication.

Modular form 151725.2.a.s

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.