Properties

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

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 206310bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.y1 206310bz1 \([1, 0, 1, -72749, -23119828]\) \(-543717769/2632500\) \(-206153668752232500\) \([]\) \(3674112\) \(2.0068\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310bz1 has rank \(1\).

Complex multiplication

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

Modular form 206310.2.a.bz

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