Properties

Label 198198.v
Number of curves $1$
Conductor $198198$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 198198.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
198198.v1 198198da1 \([1, -1, 0, -8190, -325836]\) \(-47045881/8736\) \(-11282264177184\) \([]\) \(432000\) \(1.2290\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 198198.v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 198198.v do not have complex multiplication.

Modular form 198198.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} + q^{13} - q^{14} + q^{16} + 5 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display