Properties

Label 20280.v
Number of curves $6$
Conductor $20280$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 20280.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20280.v1 20280k5 \([0, 1, 0, -540856, -153278800]\) \(1770025017602/75\) \(741397862400\) \([2]\) \(122880\) \(1.7625\)  
20280.v2 20280k3 \([0, 1, 0, -33856, -2395600]\) \(868327204/5625\) \(27802419840000\) \([2, 2]\) \(61440\) \(1.4159\)  
20280.v3 20280k6 \([0, 1, 0, -13576, -5218576]\) \(-27995042/1171875\) \(-11584341600000000\) \([2]\) \(122880\) \(1.7625\)  
20280.v4 20280k2 \([0, 1, 0, -3436, 13664]\) \(3631696/2025\) \(2502217785600\) \([2, 2]\) \(30720\) \(1.0693\)  
20280.v5 20280k1 \([0, 1, 0, -2591, 49830]\) \(24918016/45\) \(3475302480\) \([2]\) \(15360\) \(0.72275\) \(\Gamma_0(N)\)-optimal
20280.v6 20280k4 \([0, 1, 0, 13464, 121824]\) \(54607676/32805\) \(-162143712506880\) \([2]\) \(61440\) \(1.4159\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20280.v have rank \(0\).

Complex multiplication

The elliptic curves in class 20280.v do not have complex multiplication.

Modular form 20280.2.a.v

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.