Properties

Label 206310by
Number of curves $1$
Conductor $206310$
CM no
Rank $1$

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

Elliptic curves in class 206310by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.x1 206310by1 \([1, 0, 1, -1926894, -1035107408]\) \(-5344780143505321/32695650000\) \(-4840129614182850000\) \([]\) \(5913600\) \(2.4243\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 206310by do not have complex multiplication.

Modular form 206310.2.a.by

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 3 q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} + q^{12} - q^{13} - 3 q^{14} - q^{15} + q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display