↑

Properties

Label 436800.kc
Number of curves $2$
Conductor $436800$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("kc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436800.kc have rank \(1\).

Complex multiplication

The elliptic curves in class 436800.kc do not have complex multiplication.

Modular form 436800.2.a.kc

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 6 q^{11} + q^{13} - 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.kc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.kc1 436800kc2 \([0, -1, 0, -104993, -2100543]\) \(7812480469498/4400862921\) \(72103738097664000\) \([2]\) \(4718592\) \(1.9248\)  
436800.kc2 436800kc1 \([0, -1, 0, -65793, 6484257]\) \(3844850327636/22754277\) \(186403037184000\) \([2]\) \(2359296\) \(1.5782\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 436800.kc1.