Properties

Label 5200y
Number of curves 11
Conductor 52005200
CM no
Rank 11

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Show commands: SageMath
Copy content sage:E = EllipticCurve("y1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 5200y1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
5511
13131T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
33 1T+3T2 1 - T + 3 T^{2} 1.3.ab
77 1+7T2 1 + 7 T^{2} 1.7.a
1111 12T+11T2 1 - 2 T + 11 T^{2} 1.11.ac
1717 1+2T+17T2 1 + 2 T + 17 T^{2} 1.17.c
1919 1+8T+19T2 1 + 8 T + 19 T^{2} 1.19.i
2323 1+T+23T2 1 + T + 23 T^{2} 1.23.b
2929 19T+29T2 1 - 9 T + 29 T^{2} 1.29.aj
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 5200y do not have complex multiplication.

Modular form 5200.2.a.y

Copy content sage:E.q_eigenform(10)
 
qq34q72q9q11+q13+7q17+3q19+O(q20)q - q^{3} - 4 q^{7} - 2 q^{9} - q^{11} + q^{13} + 7 q^{17} + 3 q^{19} + O(q^{20}) Copy content Toggle raw display

Elliptic curves in class 5200y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5200.j1 5200y1 [0,1,0,4792,1411088][0, -1, 0, 4792, -1411088] 304175/21632304175/21632 865280000000000-865280000000000 [][] 2016020160 1.54571.5457 Γ0(N)\Gamma_0(N)-optimal