Properties

Label 333270.cs
Number of curves $1$
Conductor $333270$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333270.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.cs1 333270cs1 \([1, -1, 0, -37445364, 116070765520]\) \(-28462891429373441569/12053081880000000\) \(-2458877988571807320000000\) \([]\) \(71221248\) \(3.3879\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 333270.cs1 has rank \(1\).

Complex multiplication

The elliptic curves in class 333270.cs do not have complex multiplication.

Modular form 333270.2.a.cs

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 4q^{11} + 4q^{13} - q^{14} + q^{16} - 3q^{17} + 5q^{19} + O(q^{20})\)  Toggle raw display