Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.s1 190575bk1 \([1, -1, 1, -724505, -237755878]\) \(-30515071121161/85766121\) \(-118208496363890625\) \([]\) \(2903040\) \(2.1482\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190575.s1 has rank \(1\).

Complex multiplication

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

Modular form 190575.2.a.s

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