Properties

Label 129948h
Number of curves 44
Conductor 129948129948
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 129948h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129948.l2 129948h1 [0,1,0,154513,23325686][0, -1, 0, -154513, -23325686] 216727177216000/2738853216727177216000/2738853 51555730655525155573065552 [2][2] 414720414720 1.58551.5855 Γ0(N)\Gamma_0(N)-optimal
129948.l3 129948h2 [0,1,0,150348,24646824][0, -1, 0, -150348, -24646824] 12479332642000/1526829993-12479332642000/1526829993 45985285592692992-45985285592692992 [2][2] 829440829440 1.93211.9321  
129948.l1 129948h3 [0,1,0,242713,6293638][0, -1, 0, -242713, 6293638] 840033089536000/477272151837840033089536000/477272151837 898409462263539408898409462263539408 [2][2] 12441601244160 2.13482.1348  
129948.l4 129948h4 [0,1,0,960972,49144824][0, -1, 0, 960972, 49144824] 3258571509326000/19208431219773258571509326000/1920843121977 57852229749112850688-57852229749112850688 [2][2] 24883202488320 2.48142.4814  

Rank

sage: E.rank()
 

The elliptic curves in class 129948h have rank 00.

Complex multiplication

The elliptic curves in class 129948h do not have complex multiplication.

Modular form 129948.2.a.h

sage: E.q_eigenform(10)
 
qq3+q9q13+q172q19+O(q20)q - q^{3} + q^{9} - q^{13} + q^{17} - 2 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 Cremona numbering.

(1236216336126321)\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 Cremona labels.