Properties

Label 6720bh
Number of curves 6
Conductor 6720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6720.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.h4 6720bh1 [0, -1, 0, -2941, -60419] [2] 4096 \(\Gamma_0(N)\)-optimal
6720.h3 6720bh2 [0, -1, 0, -2961, -59535] [2, 2] 8192  
6720.h2 6720bh3 [0, -1, 0, -6881, 135681] [2, 2] 16384  
6720.h5 6720bh4 [0, -1, 0, 639, -198495] [2] 16384  
6720.h1 6720bh5 [0, -1, 0, -97601, 11765985] [2] 32768  
6720.h6 6720bh6 [0, -1, 0, 21119, 936481] [2] 32768  

Rank

sage: E.rank()
 

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

Modular form 6720.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.