Properties

Label 2142i
Number of curves $1$
Conductor $2142$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 2142i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2142.b1 2142i1 \([1, -1, 0, 9, 31]\) \(103823/714\) \(-520506\) \([]\) \(320\) \(-0.22145\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2142i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2142i do not have complex multiplication.

Modular form 2142.2.a.i

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