Properties

Label 29400.cs
Number of curves 44
Conductor 2940029400
CM no
Rank 11
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cs1")
 
E.isogeny_class()
 

Elliptic curves in class 29400.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.cs1 29400bu4 [0,1,0,3548008,2573228512][0, 1, 0, -3548008, -2573228512] 2624033547076/3241352624033547076/324135 610146537840000000610146537840000000 [2][2] 884736884736 2.43602.4360  
29400.cs2 29400bu2 [0,1,0,240508,33068512][0, 1, 0, -240508, -33068512] 3269383504/8930253269383504/893025 420253992900000000420253992900000000 [2,2][2, 2] 442368442368 2.08942.0894  
29400.cs3 29400bu1 [0,1,0,87383,9500238][0, 1, 0, -87383, 9500238] 2508888064/1181252508888064/118125 34743220312500003474322031250000 [2][2] 221184221184 1.74281.7428 Γ0(N)\Gamma_0(N)-optimal
29400.cs4 29400bu3 [0,1,0,616992,214858512][0, 1, 0, 616992, -214858512] 13799183324/1860043513799183324/18600435 35013161237040000000-35013161237040000000 [2][2] 884736884736 2.43602.4360  

Rank

sage: E.rank()
 

The elliptic curves in class 29400.cs have rank 11.

Complex multiplication

The elliptic curves in class 29400.cs do not have complex multiplication.

Modular form 29400.2.a.cs

sage: E.q_eigenform(10)
 
q+q3+q94q116q132q17+8q19+O(q20)q + q^{3} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1244212242144241)\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 LMFDB labels.