Properties

Label 81627x
Number of curves $1$
Conductor $81627$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 81627x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81627.b1 81627x1 \([0, 1, 1, -16280, -938440]\) \(-98867482624/20696067\) \(-99895962460203\) \([]\) \(691200\) \(1.4080\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 81627x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 81627x do not have complex multiplication.

Modular form 81627.2.a.x

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