Properties

Label 338130.ed
Number of curves $1$
Conductor $338130$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 338130.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.ed1 338130ed1 \([1, -1, 1, 9942268, 5283891839]\) \(6176736766011239/4260587175000\) \(-74970518132549552175000\) \([]\) \(33177600\) \(3.0779\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 338130.ed1 has rank \(1\).

Complex multiplication

The elliptic curves in class 338130.ed do not have complex multiplication.

Modular form 338130.2.a.ed

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