Properties

Label 177450.ik
Number of curves $1$
Conductor $177450$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ik1")
 
E.isogeny_class()
 

Elliptic curves in class 177450.ik

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.ik1 177450bs1 \([1, 0, 0, -424544988, -3386222727408]\) \(-112205650221491190337/745029571313664\) \(-56189303751295862784000000\) \([]\) \(86365440\) \(3.7765\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177450.ik1 has rank \(1\).

Complex multiplication

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

Modular form 177450.2.a.ik

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - q^{11} + q^{12} - q^{14} + q^{16} - 7 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display