Properties

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

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Show commands: SageMath
E = EllipticCurve("ek1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.ek1 333270ek1 \([1, -1, 1, -1202252, -581392681]\) \(-3366353209/612360\) \(-34958841396124733640\) \([]\) \(8902656\) \(2.4750\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 333270.ek1 has rank \(1\).

Complex multiplication

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

Modular form 333270.2.a.ek

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