Properties

Label 422331.a
Number of curves $1$
Conductor $422331$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 422331.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.a1 422331a1 \([0, -1, 1, -212, -1870]\) \(-53248/51\) \(-1014016731\) \([]\) \(328320\) \(0.42430\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331.a1 has rank \(2\).

Complex multiplication

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

Modular form 422331.2.a.a

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