↑

Properties

Label 140790bp
Number of curves $4$
Conductor $140790$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 140790bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.w4 140790bp1 \([1, 0, 1, -16136708, 51528743426]\) \(-9877496597620516801/18666674973573120\) \(-878190169472399148318720\) \([2]\) \(29491200\) \(3.2842\) \(\Gamma_0(N)\)-optimal
140790.w3 140790bp2 \([1, 0, 1, -328502788, 2290069019138]\) \(83333435002229316265921/67231677478118400\) \(3162973498065938350310400\) \([2, 2]\) \(58982400\) \(3.6307\)  
140790.w1 140790bp3 \([1, 0, 1, -5255026468, 146625389186306]\) \(341135431944367622806895041/222309381060000\) \(10458740686532413860000\) \([2]\) \(117964800\) \(3.9773\)  
140790.w2 140790bp4 \([1, 0, 1, -399836388, 1222575961858]\) \(150261960680978721232321/73231357863424756320\) \(3445233747511095338284717920\) \([2]\) \(117964800\) \(3.9773\)  

Rank

sage: E.rank()
 

The elliptic curves in class 140790bp have rank \(2\).

Complex multiplication

The elliptic curves in class 140790bp do not have complex multiplication.

Modular form 140790.2.a.bp

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