Properties

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

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Show commands: SageMath
E = EllipticCurve("ep1")
 
E.isogeny_class()
 

Elliptic curves in class 190575.ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.ep1 190575fe1 \([0, 0, 1, -898425, -548579969]\) \(-80621568/84035\) \(-83594587871187421875\) \([]\) \(7096320\) \(2.5180\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 190575.ep1 has rank \(1\).

Complex multiplication

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

Modular form 190575.2.a.ep

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