Properties

Label 84150.r
Number of curves $1$
Conductor $84150$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 84150.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84150.r1 84150dr1 \([1, -1, 0, 1627758, 645144916]\) \(334992828740851/320302743552\) \(-456056054784000000000\) \([]\) \(3064320\) \(2.6512\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84150.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 84150.r do not have complex multiplication.

Modular form 84150.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{7} - q^{8} + q^{11} + 3 q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display