Properties

Label 422331e
Number of curves $1$
Conductor $422331$
CM no
Rank $1$

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

Elliptic curves in class 422331e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.e1 422331e1 \([0, -1, 1, 162860, 17536014]\) \(841232384/722211\) \(-410121420385782651\) \([]\) \(5391360\) \(2.0672\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 422331e do not have complex multiplication.

Modular form 422331.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - q^{15} - 4 q^{16} + q^{17} - 2 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display