Properties

Label 349830fj
Number of curves $6$
Conductor $349830$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("349830.fj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 349830fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
349830.fj5 349830fj1 [1, -1, 1, -638852, -215464921] [2] 7077888 \(\Gamma_0(N)\)-optimal
349830.fj4 349830fj2 [1, -1, 1, -10494932, -13083562969] [2, 2] 14155776  
349830.fj3 349830fj3 [1, -1, 1, -10768712, -12364726201] [2, 2] 28311552  
349830.fj1 349830fj4 [1, -1, 1, -167918432, -837478947769] [2] 28311552  
349830.fj2 349830fj5 [1, -1, 1, -39287462, 81199588799] [2] 56623104  
349830.fj6 349830fj6 [1, -1, 1, 13369558, -59926773409] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 349830fj have rank \(1\).

Modular form 349830.2.a.fj

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.