Properties

Label 424128.e
Number of curves $1$
Conductor $424128$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 424128.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424128.e1 424128e1 \([0, -1, 0, -108977, -5216349]\) \(207474688/102789\) \(70911024924965184\) \([]\) \(4945920\) \(1.9264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 424128.e1 has rank \(2\).

Complex multiplication

The elliptic curves in class 424128.e do not have complex multiplication.

Modular form 424128.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - 3 q^{7} + q^{9} - 5 q^{11} + 2 q^{13} + 3 q^{15} - 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display