Properties

Label 19110bk
Number of curves $1$
Conductor $19110$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 19110bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.bk1 19110bk1 \([1, 0, 1, -6648, -1282172]\) \(-662989657192009/14097531093750\) \(-690779023593750\) \([]\) \(134400\) \(1.5283\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19110bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19110bk do not have complex multiplication.

Modular form 19110.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} + q^{13} + q^{15} + q^{16} - 5 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display