Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 585.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
585.a1 585g1 \([0, 0, 1, -3, 18]\) \(-4096/195\) \(-142155\) \([]\) \(96\) \(-0.33128\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 585.a1 has rank \(1\).

Complex multiplication

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

Modular form 585.2.a.a

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