Properties

Label 174928r
Number of curves $1$
Conductor $174928$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 174928r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174928.n1 174928r1 \([0, 1, 0, -13736, 643988]\) \(-235298/13\) \(-15836576098304\) \([]\) \(387072\) \(1.2906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 174928r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 174928r do not have complex multiplication.

Modular form 174928.2.a.r

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