Properties

Label 8281j
Number of curves $1$
Conductor $8281$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 8281j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8281.m1 8281j1 \([0, -1, 1, -1486, 26795]\) \(-4096\) \(-88656874579\) \([]\) \(10752\) \(0.81904\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8281j1 has rank \(1\).

Complex multiplication

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

Modular form 8281.2.a.j

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