Properties

Label 200640.e
Number of curves $8$
Conductor $200640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 200640.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200640.e1 200640ge7 \([0, -1, 0, -1371154081, 19410669138721]\) \(1087533321226184807035053481/8484255812957933638080\) \(2224096755832044555620843520\) \([2]\) \(148635648\) \(4.0760\)  
200640.e2 200640ge4 \([0, -1, 0, -1368576481, 19487758493281]\) \(1081411559614045490773061881/522522049500\) \(136976020144128000\) \([2]\) \(49545216\) \(3.5267\)  
200640.e3 200640ge6 \([0, -1, 0, -144504481, -165922487519]\) \(1272998045160051207059881/691293848290254950400\) \(181218534566200593717657600\) \([2, 2]\) \(74317824\) \(3.7294\)  
200640.e4 200640ge3 \([0, -1, 0, -111736481, -453999082719]\) \(588530213343917460371881/861551575695360000\) \(225850576259084451840000\) \([2]\) \(37158912\) \(3.3828\)  
200640.e5 200640ge2 \([0, -1, 0, -85536481, 304514237281]\) \(264020672568758737421881/5803468580250000\) \(1521344467501056000000\) \([2, 2]\) \(24772608\) \(3.1801\)  
200640.e6 200640ge5 \([0, -1, 0, -82496481, 327157981281]\) \(-236859095231405581781881/39282983014374049500\) \(-10297798299320070832128000\) \([2]\) \(49545216\) \(3.5267\)  
200640.e7 200640ge1 \([0, -1, 0, -5536481, 4402237281]\) \(71595431380957421881/9522562500000000\) \(2496282624000000000000\) \([2]\) \(12386304\) \(2.8335\) \(\Gamma_0(N)\)-optimal
200640.e8 200640ge8 \([0, -1, 0, 557857119, -1306136308959]\) \(73240740785321709623685719/45195275784938365817280\) \(-11847670375366882968805048320\) \([2]\) \(148635648\) \(4.0760\)  

Rank

sage: E.rank()
 

The elliptic curves in class 200640.e have rank \(0\).

Complex multiplication

The elliptic curves in class 200640.e do not have complex multiplication.

Modular form 200640.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} + q^{11} - 2 q^{13} + q^{15} + 6 q^{17} - q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.