Properties

Label 2420.b
Number of curves 4
Conductor 2420
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2420.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2420.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.b1 2420g4 [0, 1, 0, -859140, 306223300] [2] 25920  
2420.b2 2420g3 [0, 1, 0, -53885, 4735828] [2] 12960  
2420.b3 2420g2 [0, 1, 0, -12140, 286900] [2] 8640  
2420.b4 2420g1 [0, 1, 0, -5485, -154992] [2] 4320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2420.b have rank \(0\).

Modular form 2420.2.a.b

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

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.