Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 206310.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206310.p1 206310cg1 \([1, 1, 0, 27233, -22503419]\) \(15087533111/1488015360\) \(-220279676663255040\) \([]\) \(2534400\) \(2.0072\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206310.p1 has rank \(1\).

Complex multiplication

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

Modular form 206310.2.a.p

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