Properties

Label 106575.u
Number of curves $1$
Conductor $106575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 106575.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106575.u1 106575y1 \([1, 1, 1, -813, 24156]\) \(-77626969/293625\) \(-224806640625\) \([]\) \(82944\) \(0.86382\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 106575.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 106575.u do not have complex multiplication.

Modular form 106575.2.a.u

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