Properties

Label 1755.f
Number of curves $1$
Conductor $1755$
CM no
Rank $0$

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

Elliptic curves in class 1755.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1755.f1 1755b1 \([0, 0, 1, -4887, 141797]\) \(-72864657408/6865625\) \(-1216224871875\) \([]\) \(3780\) \(1.0608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1755.f1 has rank \(0\).

Complex multiplication

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

Modular form 1755.2.a.f

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