Properties

Label 528f
Number of curves $4$
Conductor $528$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 528f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
528.a3 528f1 \([0, -1, 0, -720, -5184]\) \(10091699281/2737152\) \(11211374592\) \([2]\) \(480\) \(0.63628\) \(\Gamma_0(N)\)-optimal
528.a4 528f2 \([0, -1, 0, 1840, -35904]\) \(168105213359/228637728\) \(-936500133888\) \([2]\) \(960\) \(0.98285\)  
528.a1 528f3 \([0, -1, 0, -161040, 24927936]\) \(112763292123580561/1932612\) \(7915978752\) \([2]\) \(2400\) \(1.4410\)  
528.a2 528f4 \([0, -1, 0, -160880, 24979776]\) \(-112427521449300721/466873642818\) \(-1912314440982528\) \([2]\) \(4800\) \(1.7876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 528f have rank \(0\).

Complex multiplication

The elliptic curves in class 528f do not have complex multiplication.

Modular form 528.2.a.f

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.