Properties

Label 2800h
Number of curves 11
Conductor 28002800
CM no
Rank 00

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 2800h1 has rank 00.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
5511
771+T1 + T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
33 1+T+3T2 1 + T + 3 T^{2} 1.3.b
1111 1+3T+11T2 1 + 3 T + 11 T^{2} 1.11.d
1313 12T+13T2 1 - 2 T + 13 T^{2} 1.13.ac
1717 13T+17T2 1 - 3 T + 17 T^{2} 1.17.ad
1919 17T+19T2 1 - 7 T + 19 T^{2} 1.19.ah
2323 1+23T2 1 + 23 T^{2} 1.23.a
2929 1+6T+29T2 1 + 6 T + 29 T^{2} 1.29.g
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 2800h do not have complex multiplication.

Modular form 2800.2.a.h

Copy content sage:E.q_eigenform(10)
 
q3q3+q7+6q9+5q11+5q13+7q17+2q19+O(q20)q - 3 q^{3} + q^{7} + 6 q^{9} + 5 q^{11} + 5 q^{13} + 7 q^{17} + 2 q^{19} + O(q^{20}) Copy content Toggle raw display

Elliptic curves in class 2800h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.c1 2800h1 [0,0,0,10300,414500][0, 0, 0, -10300, -414500] 30211716096/1071875-30211716096/1071875 4287500000000-4287500000000 [][] 1152011520 1.19621.1962 Γ0(N)\Gamma_0(N)-optimal