Properties

Label 163995.a
Number of curves $1$
Conductor $163995$
CM no
Rank $1$

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

Elliptic curves in class 163995.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163995.a1 163995f1 \([0, -1, 1, -55786, -7948704]\) \(-32278933504/27421875\) \(-16311170755546875\) \([]\) \(2107392\) \(1.8085\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163995.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 163995.a do not have complex multiplication.

Modular form 163995.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - q^{7} + q^{9} + 2 q^{10} - 5 q^{11} - 2 q^{12} - q^{13} + 2 q^{14} + q^{15} - 4 q^{16} + 7 q^{17} - 2 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display