Properties

Label 111090.f
Number of curves $1$
Conductor $111090$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 111090.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111090.f1 111090c1 \([1, 1, 0, -133583, -38127963]\) \(-3366353209/6048000\) \(-473624838979488000\) \([]\) \(1589760\) \(2.0818\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 111090.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 111090.f do not have complex multiplication.

Modular form 111090.2.a.f

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