Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 206310.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.s1 206310bt1 \([1, 0, 1, -13501549309, 603841163747096]\) \(-151120718047387272165983/345948408000\) \(-623105895798087800904000\) \([]\) \(218909952\) \(4.2361\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310.s1 has rank \(1\).

Complex multiplication

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

Modular form 206310.2.a.s

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