Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 422331bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.bg1 422331bg1 \([0, 1, 1, 29519005, -55831662337]\) \(5009339741732864/5271114033171\) \(-2993303583439634633452011\) \([]\) \(58595328\) \(3.3833\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331bg1 has rank \(1\).

Complex multiplication

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

Modular form 422331.2.a.bg

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