Properties

Label 20400.cs
Number of curves 11
Conductor 2040020400
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("cs1")
 
E.isogeny_class()
 

Elliptic curves in class 20400.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20400.cs1 20400bf1 [0,1,0,5508,160137][0, 1, 0, -5508, -160137] 73934023936/516375-73934023936/516375 129093750000-129093750000 [][] 2304023040 0.965480.96548 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20400.cs1 has rank 11.

Complex multiplication

The elliptic curves in class 20400.cs do not have complex multiplication.

Modular form 20400.2.a.cs

sage: E.q_eigenform(10)
 
q+q3q7+q9+3q11+4q13+q17+5q19+O(q20)q + q^{3} - q^{7} + q^{9} + 3 q^{11} + 4 q^{13} + q^{17} + 5 q^{19} + O(q^{20}) Copy content Toggle raw display