Properties

Label 193200.b
Number of curves $1$
Conductor $193200$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 193200.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.b1 193200hd1 \([0, -1, 0, 352, 2832]\) \(187878620/255507\) \(-6540979200\) \([]\) \(117504\) \(0.56918\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 193200.b1 has rank \(2\).

Complex multiplication

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

Modular form 193200.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 5 q^{11} + 2 q^{13} - 2 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display