Properties

Label 206310.z
Number of curves $1$
Conductor $206310$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 206310.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.z1 206310bn1 \([1, 0, 1, -138, 1888]\) \(-543717769/2632500\) \(-1392592500\) \([]\) \(159744\) \(0.43906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310.z1 has rank \(2\).

Complex multiplication

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

Modular form 206310.2.a.z

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