Properties

Label 39984bs
Number of curves $4$
Conductor $39984$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39984bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39984.bl4 39984bs1 \([0, -1, 0, 768, 2211840]\) \(103823/4386816\) \(-2113964095832064\) \([2]\) \(221184\) \(1.6195\) \(\Gamma_0(N)\)-optimal
39984.bl3 39984bs2 \([0, -1, 0, -250112, 47370240]\) \(3590714269297/73410624\) \(35375867916189696\) \([2, 2]\) \(442368\) \(1.9661\)  
39984.bl2 39984bs3 \([0, -1, 0, -532352, -78847488]\) \(34623662831857/14438442312\) \(6957745355016142848\) \([2]\) \(884736\) \(2.3127\)  
39984.bl1 39984bs4 \([0, -1, 0, -3981952, 3059711488]\) \(14489843500598257/6246072\) \(3009921534885888\) \([2]\) \(884736\) \(2.3127\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39984bs have rank \(1\).

Complex multiplication

The elliptic curves in class 39984bs do not have complex multiplication.

Modular form 39984.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} + q^{9} + 6q^{13} - 2q^{15} - q^{17} + O(q^{20})\)  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.