Properties

Label 52983a
Number of curves 66
Conductor 5298352983
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 52983a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52983.e6 52983a1 [1,1,1,7411,52260][1, -1, 1, 7411, 52260] 103823/63103823/63 27318450663567-27318450663567 [2][2] 100352100352 1.26741.2674 Γ0(N)\Gamma_0(N)-optimal
52983.e5 52983a2 [1,1,1,30434,445848][1, -1, 1, -30434, 445848] 7189057/39697189057/3969 17210623918047211721062391804721 [2,2][2, 2] 200704200704 1.61401.6140  
52983.e3 52983a3 [1,1,1,295349,61332330][1, -1, 1, -295349, -61332330] 6570725617/459276570725617/45927 1991515053374034319915150533740343 [2][2] 401408401408 1.96061.9606  
52983.e2 52983a4 [1,1,1,371039,86959518][1, -1, 1, -371039, 86959518] 13027640977/2160913027640977/21609 93702285776034819370228577603481 [2,2][2, 2] 401408401408 1.96061.9606  
52983.e4 52983a5 [1,1,1,257504,141093006][1, -1, 1, -257504, 141093006] 4354703137/17294403-4354703137/17294403 7499306271608652627-7499306271608652627 [2][2] 802816802816 2.30722.3072  
52983.e1 52983a6 [1,1,1,5934254,5565613650][1, -1, 1, -5934254, 5565613650] 53297461115137/14753297461115137/147 6374305154832363743051548323 [2][2] 802816802816 2.30722.3072  

Rank

sage: E.rank()
 

The elliptic curves in class 52983a have rank 00.

Complex multiplication

The elliptic curves in class 52983a do not have complex multiplication.

Modular form 52983.2.a.a

sage: E.q_eigenform(10)
 
qq2q4+2q5q7+3q82q10+4q112q13+q14q166q174q19+O(q20)q - q^{2} - q^{4} + 2 q^{5} - q^{7} + 3 q^{8} - 2 q^{10} + 4 q^{11} - 2 q^{13} + q^{14} - q^{16} - 6 q^{17} - 4 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.

(124488212244421488424122848214848241)\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.