Properties

Label 39984.r
Number of curves $1$
Conductor $39984$
CM no
Rank $1$

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

Elliptic curves in class 39984.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39984.r1 39984bn1 \([0, -1, 0, 264, 624]\) \(10100279/6936\) \(-1392082944\) \([]\) \(17280\) \(0.44311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 39984.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 39984.r do not have complex multiplication.

Modular form 39984.2.a.r

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