Properties

Label 262080.c
Number of curves 4
Conductor 262080
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("262080.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.c1 262080c3 [0, 0, 0, -29648748, -62138026928] [2] 15925248  
262080.c2 262080c4 [0, 0, 0, -29487468, -62847465392] [2] 31850496  
262080.c3 262080c1 [0, 0, 0, -436908, -49912112] [2] 5308416 \(\Gamma_0(N)\)-optimal
262080.c4 262080c2 [0, 0, 0, 1538772, -376294448] [2] 10616832  

Rank

sage: E.rank()
 

The elliptic curves in class 262080.c have rank \(1\).

Modular form 262080.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 6q^{11} - q^{13} + 8q^{19} + O(q^{20}) \)

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.