Properties

Label 32340.j
Number of curves $4$
Conductor $32340$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.j1 32340n4 \([0, -1, 0, -2430220, -768028568]\) \(52702650535889104/22020583921875\) \(663219117523116000000\) \([2]\) \(1492992\) \(2.6924\)  
32340.j2 32340n2 \([0, -1, 0, -2095060, -1166495000]\) \(33766427105425744/9823275\) \(295858811001600\) \([2]\) \(497664\) \(2.1431\)  
32340.j3 32340n1 \([0, -1, 0, -130405, -18350618]\) \(-130287139815424/2250652635\) \(-4236592509681840\) \([2]\) \(248832\) \(1.7965\) \(\Gamma_0(N)\)-optimal
32340.j4 32340n3 \([0, -1, 0, 504635, -88316150]\) \(7549996227362816/6152409907875\) \(-11581197972025374000\) \([2]\) \(746496\) \(2.3458\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32340.j have rank \(0\).

Complex multiplication

The elliptic curves in class 32340.j do not have complex multiplication.

Modular form 32340.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{11} - 2q^{13} - q^{15} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.