Properties

Label 489762.p
Number of curves $1$
Conductor $489762$
CM no
Rank $0$

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

Elliptic curves in class 489762.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489762.p1 489762p1 \([1, -1, 0, 179622, 176349460]\) \(5202195898618823/112114092318816\) \(-13812568287770450016\) \([]\) \(10321920\) \(2.3530\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 489762.p1 has rank \(0\).

Complex multiplication

The elliptic curves in class 489762.p do not have complex multiplication.

Modular form 489762.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{7} - q^{8} + 2 q^{10} + q^{14} + q^{16} + 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display