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Properties

Label 494209.g
Number of curves $1$
Conductor $494209$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("g1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 494209.g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 494209.g do not have complex multiplication.

Modular form 494209.2.a.g

Copy content sage:E.q_eigenform(10)
 
\(q - 3 q^{3} - 2 q^{4} + 2 q^{5} - q^{7} + 6 q^{9} + 3 q^{11} + 6 q^{12} + 6 q^{13} - 6 q^{15} + 4 q^{16} - 2 q^{17} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 494209.g

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
494209.g1 494209g1 \([0, 0, 1, -363737824, -367319233071]\) \(44091731607552/25033168477\) \(3021675145596260523149395933\) \([]\) \(354585600\) \(3.9629\) \(\Gamma_0(N)\)-optimal