Properties

Label 286650dd
Number of curves 11
Conductor 286650286650
CM no
Rank 11

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 286650dd1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
221+T1 + T
3311
5511
7711
13131T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
1111 1+T+11T2 1 + T + 11 T^{2} 1.11.b
1717 1+7T+17T2 1 + 7 T + 17 T^{2} 1.17.h
1919 13T+19T2 1 - 3 T + 19 T^{2} 1.19.ad
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 14T+29T2 1 - 4 T + 29 T^{2} 1.29.ae
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 286650dd do not have complex multiplication.

Modular form 286650.2.a.dd

Copy content sage:E.q_eigenform(10)
 
qq2+q4q8q11+q13+q167q17+3q19+O(q20)q - q^{2} + q^{4} - q^{8} - q^{11} + q^{13} + q^{16} - 7 q^{17} + 3 q^{19} + O(q^{20}) Copy content Toggle raw display

Elliptic curves in class 286650dd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286650.dd1 286650dd1 [1,1,0,5283,1630341][1, -1, 0, 5283, 1630341] 304175/21632304175/21632 1159557955920000-1159557955920000 [][] 14515201451520 1.57011.5701 Γ0(N)\Gamma_0(N)-optimal