Properties

Label 2093i
Number of curves $1$
Conductor $2093$
CM no
Rank $1$

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

Elliptic curves in class 2093i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2093.b1 2093i1 \([0, -1, 1, 0, -6]\) \(-4096/14651\) \(-14651\) \([]\) \(192\) \(-0.52170\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2093i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2093i do not have complex multiplication.

Modular form 2093.2.a.i

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