Properties

Label 6720.g
Number of curves 4
Conductor 6720
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("6720.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.g1 6720a3 [0, -1, 0, -56481, -5147775] [2] 12288  
6720.g2 6720a4 [0, -1, 0, -8961, 221121] [2] 12288  
6720.g3 6720a2 [0, -1, 0, -3561, -78039] [2, 2] 6144  
6720.g4 6720a1 [0, -1, 0, 84, -4410] [2] 3072 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6720.g have rank \(1\).

Modular form 6720.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} - 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.