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Properties

Label 459186x
Number of curves $1$
Conductor $459186$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("x1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 459186x1 has rank \(0\).

Complex multiplication

The elliptic curves in class 459186x do not have complex multiplication.

Modular form 459186.2.a.x

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{10} + 5 q^{11} - q^{12} + q^{13} - q^{14} - 3 q^{15} + q^{16} + 8 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 459186x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459186.x1 459186x1 \([1, 1, 0, -2425461, -1695597267]\) \(-2231078688265767817/462825029581824\) \(-327347349747662060544\) \([]\) \(30240000\) \(2.6584\) \(\Gamma_0(N)\)-optimal