Properties

Label 6720g
Number of curves $4$
Conductor $6720$
CM no
Rank $0$
Graph

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

Elliptic curves in class 6720g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.p3 6720g1 \([0, -1, 0, -161, 801]\) \(1771561/105\) \(27525120\) \([2]\) \(2048\) \(0.18061\) \(\Gamma_0(N)\)-optimal
6720.p2 6720g2 \([0, -1, 0, -481, -2975]\) \(47045881/11025\) \(2890137600\) \([2, 2]\) \(4096\) \(0.52719\)  
6720.p1 6720g3 \([0, -1, 0, -7201, -232799]\) \(157551496201/13125\) \(3440640000\) \([2]\) \(8192\) \(0.87376\)  
6720.p4 6720g4 \([0, -1, 0, 1119, -19935]\) \(590589719/972405\) \(-254910136320\) \([2]\) \(8192\) \(0.87376\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 6720g do not have complex multiplication.

Modular form 6720.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.