Properties

Label 197.a
Number of curves $1$
Conductor $197$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 197.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
197.a1 197a1 \([0, 0, 1, -5, 4]\) \(13824000/197\) \(197\) \([]\) \(10\) \(-0.75527\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 197.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 197.a do not have complex multiplication.

Modular form 197.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - 3 q^{7} - 3 q^{9} + 4 q^{11} - 2 q^{13} + 6 q^{14} - 4 q^{16} - 8 q^{17} + 6 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display