Properties

Label 489762ei
Number of curves $1$
Conductor $489762$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ei1")
 
E.isogeny_class()
 

Elliptic curves in class 489762ei

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489762.ei1 489762ei1 \([1, -1, 1, -935447, 349656207]\) \(-25727239787761/101406816\) \(-356824601122874976\) \([]\) \(6739200\) \(2.2256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 489762ei1 has rank \(1\).

Complex multiplication

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

Modular form 489762.2.a.ei

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