Properties

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

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Show commands: SageMath
E = EllipticCurve("hf1")
 
E.isogeny_class()
 

Elliptic curves in class 193200hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.i1 193200hf1 \([0, -1, 0, 42917, -7474838]\) \(55947622400/186264603\) \(-29103844218750000\) \([]\) \(1330560\) \(1.8422\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 193200hf1 has rank \(0\).

Complex multiplication

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

Modular form 193200.2.a.hf

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 3 q^{11} - 2 q^{13} + 4 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display