Properties

Label 164730.g
Number of curves $1$
Conductor $164730$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 164730.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.g1 164730dd1 \([1, 1, 0, 3437, -13907]\) \(15529841222759/9338880000\) \(-2698936320000\) \([]\) \(311040\) \(1.0746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 164730.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 164730.g do not have complex multiplication.

Modular form 164730.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} - 2 q^{13} + 2 q^{14} + q^{15} + q^{16} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display