Properties

Label 103428.b
Number of curves 11
Conductor 103428103428
CM no
Rank 11

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Show commands: SageMath
Copy content sage:E = EllipticCurve("b1") E.isogeny_class()
 

Elliptic curves in class 103428.b

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103428.b1 103428n1 [0,0,0,624,6019][0, 0, 0, -624, -6019] 13631488/51-13631488/51 100532016-100532016 [][] 3571235712 0.395310.39531 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 103428.b1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
131311
17171+T1 + T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
55 1+3T+5T2 1 + 3 T + 5 T^{2} 1.5.d
77 1+4T+7T2 1 + 4 T + 7 T^{2} 1.7.e
1111 1T+11T2 1 - T + 11 T^{2} 1.11.ab
1919 1+4T+19T2 1 + 4 T + 19 T^{2} 1.19.e
2323 1+3T+23T2 1 + 3 T + 23 T^{2} 1.23.d
2929 1+3T+29T2 1 + 3 T + 29 T^{2} 1.29.d
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 103428.b do not have complex multiplication.

Modular form 103428.2.a.b

Copy content sage:E.q_eigenform(10)
 
q3q54q7+q11q174q19+O(q20)q - 3 q^{5} - 4 q^{7} + q^{11} - q^{17} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display