Properties

Label 197106by
Number of curves $1$
Conductor $197106$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 197106by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
197106.be1 197106by1 \([1, 0, 1, -36274732, 84569973098]\) \(-112205650221491190337/745029571313664\) \(-35050572553503650217984\) \([]\) \(34186320\) \(3.1615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 197106by1 has rank \(0\).

Complex multiplication

The elliptic curves in class 197106by do not have complex multiplication.

Modular form 197106.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{10} + q^{11} + q^{12} + q^{13} + q^{14} + 3 q^{15} + q^{16} + 7 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display