Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.f1 333270f1 \([1, -1, 0, -19808597655, -1412114152496099]\) \(-28462891429373441569/12053081880000000\) \(-364002188980759336952907480000000\) \([]\) \(1638088704\) \(4.9557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 333270.f1 has rank \(1\).

Complex multiplication

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

Modular form 333270.2.a.f

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