Properties

Label 6720.p
Number of curves 4
Conductor 6720
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("6720.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.p1 6720g3 [0, -1, 0, -7201, -232799] [2] 8192  
6720.p2 6720g2 [0, -1, 0, -481, -2975] [2, 2] 4096  
6720.p3 6720g1 [0, -1, 0, -161, 801] [2] 2048 \(\Gamma_0(N)\)-optimal
6720.p4 6720g4 [0, -1, 0, 1119, -19935] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 6720.p have rank \(0\).

Modular form 6720.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} + 6q^{13} + q^{15} + 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.