Properties

Label 116886.d
Number of curves $1$
Conductor $116886$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.d1 116886e1 \([1, 1, 0, 41017, 384531]\) \(4307673070511/2525789574\) \(-4474590303505014\) \([]\) \(691200\) \(1.6925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 116886.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 116886.d do not have complex multiplication.

Modular form 116886.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} - 4q^{17} - q^{18} + 6q^{19} + O(q^{20})\)  Toggle raw display