Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("6720.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.i1 6720d4 [0, -1, 0, -2721, 55521] [2] 4096  
6720.i2 6720d3 [0, -1, 0, -1601, -23775] [2] 4096  
6720.i3 6720d2 [0, -1, 0, -201, 585] [2, 2] 2048  
6720.i4 6720d1 [0, -1, 0, 44, 46] [2] 1024 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 6720.2.a.i

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

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.