Properties

Label 392784p
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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

Elliptic curves in class 392784p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.p1 392784p1 \([0, -1, 0, -51221, -2781603]\) \(12845056/4509\) \(5216996957147136\) \([]\) \(1632960\) \(1.7172\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 392784p do not have complex multiplication.

Modular form 392784.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} + q^{15} + 5 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display