Properties

Label 416160.r
Number of curves $1$
Conductor $416160$
CM no
Rank $1$

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

Elliptic curves in class 416160.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416160.r1 416160r1 \([0, 0, 0, 165597, -20860598]\) \(55742968/53125\) \(-478619028187200000\) \([]\) \(4147200\) \(2.0796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 416160.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416160.r do not have complex multiplication.

Modular form 416160.2.a.r

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