Properties

Label 190575b
Number of curves $1$
Conductor $190575$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 190575b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.a1 190575b1 \([0, 0, 1, -335775, -64794744]\) \(5186867200/754677\) \(609150732775633125\) \([]\) \(3870720\) \(2.1377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190575b1 has rank \(2\).

Complex multiplication

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

Modular form 190575.2.a.b

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