Properties

Label 585.b
Number of curves $1$
Conductor $585$
CM no
Rank $0$

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

Elliptic curves in class 585.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
585.b1 585e1 \([0, 0, 1, -1713, -28022]\) \(-762549907456/24024195\) \(-17513638155\) \([]\) \(672\) \(0.74187\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 585.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 585.b do not have complex multiplication.

Modular form 585.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - q^{5} + 3 q^{7} + 2 q^{10} + q^{11} - q^{13} - 6 q^{14} - 4 q^{16} + q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display