Properties

Label 145794.q
Number of curves $2$
Conductor $145794$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 145794.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145794.q1 145794t2 \([1, 0, 1, -2003210711, 34509283628546]\) \(16901491583223625/862488\) \(45366120363816587301912\) \([]\) \(54577152\) \(3.8207\)  
145794.q2 145794t1 \([1, 0, 1, -26939906, 38377739414]\) \(41108661625/11691702\) \(614973379559918655553398\) \([]\) \(18192384\) \(3.2714\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145794.q have rank \(0\).

Complex multiplication

The elliptic curves in class 145794.q do not have complex multiplication.

Modular form 145794.2.a.q

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.