Properties

Label 1755.b
Number of curves $1$
Conductor $1755$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1755.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1755.b1 1755f1 \([0, 0, 1, 3, 0]\) \(110592/65\) \(-1755\) \([]\) \(120\) \(-0.68809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1755.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1755.b do not have complex multiplication.

Modular form 1755.2.a.b

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