Properties

Label 392784.s
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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

Elliptic curves in class 392784.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.s1 392784s1 \([0, -1, 0, -5553, 188973]\) \(-30814336000/6777027\) \(-4165540307712\) \([]\) \(493440\) \(1.1421\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784.s1 has rank \(1\).

Complex multiplication

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

Modular form 392784.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 2 q^{11} - q^{13} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display