Properties

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

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

Elliptic curves in class 585.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
585.c1 585i1 \([0, 0, 1, -597, 8820]\) \(-32278933504/27421875\) \(-19990546875\) \([]\) \(672\) \(0.67416\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 585.c1 has rank \(1\).

Complex multiplication

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

Modular form 585.2.a.c

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