Properties

Label 3520.bd
Number of curves 4
Conductor 3520
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("3520.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3520.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3520.bd1 3520g4 [0, -1, 0, -28401, -1832815] [2] 6912  
3520.bd2 3520g3 [0, -1, 0, -1781, -27979] [2] 3456  
3520.bd3 3520g2 [0, -1, 0, -401, -1615] [2] 2304  
3520.bd4 3520g1 [0, -1, 0, -181, 981] [2] 1152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3520.bd have rank \(0\).

Modular form 3520.2.a.bd

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} - 4q^{7} + q^{9} + q^{11} + 4q^{13} - 2q^{15} + 4q^{19} + O(q^{20}) \)

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.