Properties

Label 46200bx
Number of curves $4$
Conductor $46200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 46200bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.u3 46200bx1 \([0, -1, 0, -1783, 25312]\) \(2508888064/396165\) \(99041250000\) \([4]\) \(36864\) \(0.83266\) \(\Gamma_0(N)\)-optimal
46200.u2 46200bx2 \([0, -1, 0, -7908, -244188]\) \(13674725584/1334025\) \(5336100000000\) \([2, 2]\) \(73728\) \(1.1792\)  
46200.u4 46200bx3 \([0, -1, 0, 9592, -1189188]\) \(6099383804/41507235\) \(-664115760000000\) \([2]\) \(147456\) \(1.5258\)  
46200.u1 46200bx4 \([0, -1, 0, -123408, -16645188]\) \(12990838708516/144375\) \(2310000000000\) \([2]\) \(147456\) \(1.5258\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46200bx have rank \(1\).

Complex multiplication

The elliptic curves in class 46200bx do not have complex multiplication.

Modular form 46200.2.a.bx

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - q^{11} - 2 q^{13} - 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.