Properties

Label 435600.fs
Number of curves $4$
Conductor $435600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("fs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 435600.fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.fs1 435600fs4 \([0, 0, 0, -6806150175, 216122709888250]\) \(6749703004355978704/5671875\) \(29300179546687500000000\) \([2]\) \(159252480\) \(4.0465\) \(\Gamma_0(N)\)-optimal*
435600.fs2 435600fs3 \([0, 0, 0, -425290800, 3378477466375]\) \(-26348629355659264/24169921875\) \(-7803669978698730468750000\) \([2]\) \(79626240\) \(3.7000\) \(\Gamma_0(N)\)-optimal*
435600.fs3 435600fs2 \([0, 0, 0, -85931175, 282320739250]\) \(13584145739344/1195803675\) \(6177368573899944300000000\) \([2]\) \(53084160\) \(3.4972\) \(\Gamma_0(N)\)-optimal*
435600.fs4 435600fs1 \([0, 0, 0, 5953200, 20542154875]\) \(72268906496/606436875\) \(-195798449820739218750000\) \([2]\) \(26542080\) \(3.1506\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 435600.fs1.

Rank

sage: E.rank()
 

The elliptic curves in class 435600.fs have rank \(0\).

Complex multiplication

The elliptic curves in class 435600.fs do not have complex multiplication.

Modular form 435600.2.a.fs

sage: E.q_eigenform(10)
 
\(q - 2q^{7} + 2q^{13} + 2q^{19} + O(q^{20})\)  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.