Properties

Label 190575.bf
Number of curves $1$
Conductor $190575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.bf1 190575bc1 \([1, -1, 1, 19645, -186128]\) \(1382658525/823543\) \(-499426843348125\) \([]\) \(677376\) \(1.5097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190575.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 190575.bf do not have complex multiplication.

Modular form 190575.2.a.bf

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