Properties

Label 195083.f
Number of curves $1$
Conductor $195083$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 195083.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195083.f1 195083f1 \([1, 0, 0, -20, 54029]\) \(-1/1421\) \(-1261142730701\) \([]\) \(234000\) \(1.0008\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 195083.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 195083.f do not have complex multiplication.

Modular form 195083.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + q^{7} + 3 q^{8} - 2 q^{9} - q^{10} + 5 q^{11} - q^{12} + 5 q^{13} - q^{14} + q^{15} - q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display