Properties

Label 206400.hg
Number of curves $1$
Conductor $206400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hg1")
 
E.isogeny_class()
 

Elliptic curves in class 206400.hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206400.hg1 206400gu1 \([0, 1, 0, 109639167, 428298170463]\) \(56935209711531575/63898719879168\) \(-163580722890670080000000000\) \([]\) \(58291200\) \(3.7164\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 206400.hg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 206400.hg do not have complex multiplication.

Modular form 206400.2.a.hg

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - 4 q^{11} + 4 q^{13} - 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display