Properties

Label 193200hg
Number of curves $1$
Conductor $193200$
CM no
Rank $0$

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

Elliptic curves in class 193200hg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.l1 193200hg1 \([0, -1, 0, -235208, 48318912]\) \(-143906968900/17253243\) \(-172532430000000000\) \([]\) \(2177280\) \(2.0428\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 193200hg1 has rank \(0\).

Complex multiplication

The elliptic curves in class 193200hg do not have complex multiplication.

Modular form 193200.2.a.hg

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} + 6 q^{13} + 2 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display