Properties

Label 19404.p
Number of curves $1$
Conductor $19404$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 19404.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19404.p1 19404y1 \([0, 0, 0, 6027, -59339]\) \(17643776/11319\) \(-15532587577584\) \([]\) \(27648\) \(1.2201\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19404.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 19404.p do not have complex multiplication.

Modular form 19404.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{11} + 3 q^{13} + 2 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display