Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193200.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.cs1 193200dy1 \([0, -1, 0, -28133, 1828137]\) \(-615640662016/978075\) \(-3912300000000\) \([]\) \(506880\) \(1.3142\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 193200.cs1 has rank \(1\).

Complex multiplication

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

Modular form 193200.2.a.cs

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