Properties

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

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

Elliptic curves in class 193200.hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.hf1 193200bp1 \([0, 1, 0, 7387, 83058]\) \(111431820247040/71501334387\) \(-28600533754800\) \([]\) \(608832\) \(1.2710\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 193200.hf1 has rank \(1\).

Complex multiplication

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

Modular form 193200.2.a.hf

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + 3 q^{11} + 4 q^{13} - 8 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display