Properties

Label 3825.k
Number of curves 11
Conductor 38253825
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 3825.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3825.k1 3825g1 [1,1,0,27,54][1, -1, 0, -27, -54] 121945/17-121945/17 309825-309825 [][] 360360 0.21489-0.21489 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3825.k1 has rank 11.

Complex multiplication

The elliptic curves in class 3825.k do not have complex multiplication.

Modular form 3825.2.a.k

sage: E.q_eigenform(10)
 
q+q2q4q73q8+4q11+q13q14q16+q176q19+O(q20)q + q^{2} - q^{4} - q^{7} - 3 q^{8} + 4 q^{11} + q^{13} - q^{14} - q^{16} + q^{17} - 6 q^{19} + O(q^{20}) Copy content Toggle raw display