Properties

Label 80850.fq
Number of curves 4
Conductor 80850
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("80850.fq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 80850.fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
80850.fq1 80850gb3 [1, 0, 0, -98638, 11869892] [2] 622080  
80850.fq2 80850gb4 [1, 0, 0, -49638, 23678892] [2] 1244160  
80850.fq3 80850gb1 [1, 0, 0, -6763, -202483] [2] 207360 \(\Gamma_0(N)\)-optimal
80850.fq4 80850gb2 [1, 0, 0, 5487, -851733] [2] 414720  

Rank

sage: E.rank()
 

The elliptic curves in class 80850.fq have rank \(0\).

Modular form 80850.2.a.fq

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.