Properties

Label 226512.et
Number of curves 11
Conductor 226512226512
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 226512.et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
226512.et1 226512cl1 [0,0,0,20635824,36088776592][0, 0, 0, -20635824, -36088776592] 1518309117952/369603-1518309117952/369603 236572601242841690112-236572601242841690112 [][] 1182720011827200 2.89792.8979 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 226512.et1 has rank 11.

Complex multiplication

The elliptic curves in class 226512.et do not have complex multiplication.

Modular form 226512.2.a.et

sage: E.q_eigenform(10)
 
q+2q53q7+q13+q19+O(q20)q + 2 q^{5} - 3 q^{7} + q^{13} + q^{19} + O(q^{20}) Copy content Toggle raw display