Properties

Label 43560q
Number of curves 4
Conductor 43560
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("43560.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43560q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43560.bd3 43560q1 [0, 0, 0, -2178, 35937] [2] 40960 \(\Gamma_0(N)\)-optimal
43560.bd2 43560q2 [0, 0, 0, -7623, -215622] [2, 2] 81920  
43560.bd4 43560q3 [0, 0, 0, 14157, -1221858] [2] 163840  
43560.bd1 43560q4 [0, 0, 0, -116523, -15309162] [2] 163840  

Rank

sage: E.rank()
 

The elliptic curves in class 43560q have rank \(1\).

Modular form 43560.2.a.bd

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{7} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 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.