Properties

Label 5040.i
Number of curves $6$
Conductor $5040$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5040.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.i1 5040bg5 [0, 0, 0, -2419203, -1448293502] [2] 49152  
5040.i2 5040bg3 [0, 0, 0, -151203, -22628702] [2, 2] 24576  
5040.i3 5040bg6 [0, 0, 0, -141123, -25775678] [2] 49152  
5040.i4 5040bg4 [0, 0, 0, -53283, 4474402] [2] 24576  
5040.i5 5040bg2 [0, 0, 0, -10083, -303518] [2, 2] 12288  
5040.i6 5040bg1 [0, 0, 0, 1437, -29342] [2] 6144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5040.i have rank \(1\).

Modular form 5040.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.