Properties

Label 248430.ee
Number of curves $6$
Conductor $248430$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("248430.ee1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430.ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.ee1 248430ee5 [1, 0, 1, -74653388, 248262691016] [2] 33030144  
248430.ee2 248430ee4 [1, 0, 1, -6997618, -7119771592] [2] 16515072  
248430.ee3 248430ee3 [1, 0, 1, -4678938, 3855932056] [2, 2] 16515072  
248430.ee4 248430ee6 [1, 0, 1, -952488, 9830176696] [2] 33030144  
248430.ee5 248430ee2 [1, 0, 1, -538438, -56012344] [2, 2] 8257536  
248430.ee6 248430ee1 [1, 0, 1, 124042, -6723832] [2] 4128768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 248430.ee have rank \(0\).

Modular form 248430.2.a.ee

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + q^{15} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.