Properties

Label 459.c
Number of curves 11
Conductor 459459
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 459.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459.c1 459h1 [1,1,1,2,28][1, -1, 1, -2, 28] 27/17-27/17 334611-334611 [][] 3636 0.26087-0.26087 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 459.c1 has rank 11.

Complex multiplication

The elliptic curves in class 459.c do not have complex multiplication.

Modular form 459.2.a.c

sage: E.q_eigenform(10)
 
qq2q4+q52q7+3q8q105q13+2q14q16+q17q19+O(q20)q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 3 q^{8} - q^{10} - 5 q^{13} + 2 q^{14} - q^{16} + q^{17} - q^{19} + O(q^{20}) Copy content Toggle raw display