Properties

Label 32340.s
Number of curves $4$
Conductor $32340$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.s1 32340s4 \([0, -1, 0, -12249820, 16506315400]\) \(6749703004355978704/5671875\) \(170826348000000\) \([2]\) \(622080\) \(2.4665\)  
32340.s2 32340s3 \([0, -1, 0, -765445, 258221650]\) \(-26348629355659264/24169921875\) \(-45497074218750000\) \([2]\) \(311040\) \(2.1199\)  
32340.s3 32340s2 \([0, -1, 0, -154660, 21608392]\) \(13584145739344/1195803675\) \(36015387279379200\) \([2]\) \(207360\) \(1.9172\)  
32340.s4 32340s1 \([0, -1, 0, 10715, 1564942]\) \(72268906496/606436875\) \(-1141547070510000\) \([2]\) \(103680\) \(1.5706\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.s have rank \(1\).

Complex multiplication

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

Modular form 32340.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.