Properties

Label 8281.i
Number of curves $1$
Conductor $8281$
CM no
Rank $1$

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

Elliptic curves in class 8281.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8281.i1 8281a1 \([1, -1, 0, -47098, -2131193]\) \(2457\) \(4702525276151521\) \([]\) \(72072\) \(1.7049\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8281.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8281.i do not have complex multiplication.

Modular form 8281.2.a.i

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