Properties

Label 177450im
Number of curves $1$
Conductor $177450$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("im1")
 
E.isogeny_class()
 

Elliptic curves in class 177450im

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.x1 177450im1 \([1, 1, 0, -8460650, 10401995700]\) \(-22202140659489025/2656521215712\) \(-8014075320431014380000\) \([]\) \(13547520\) \(2.9384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177450im1 has rank \(0\).

Complex multiplication

The elliptic curves in class 177450im do not have complex multiplication.

Modular form 177450.2.a.im

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