Properties

Label 79420b
Number of curves 4
Conductor 79420
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("79420.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 79420b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
79420.e4 79420b1 [0, -1, 0, -16365, -783838] [2] 248832 \(\Gamma_0(N)\)-optimal
79420.e3 79420b2 [0, -1, 0, -36220, 1511400] [2] 497664  
79420.e2 79420b3 [0, -1, 0, -160765, 24551142] [2] 746496  
79420.e1 79420b4 [0, -1, 0, -2563220, 1580381000] [2] 1492992  

Rank

sage: E.rank()
 

The elliptic curves in class 79420b have rank \(0\).

Modular form 79420.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.