Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 422331g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.g1 422331g1 \([0, 1, 1, -117460464, -489993818128]\) \(6441016595550208/511270461\) \(14226403939657635784149\) \([]\) \(99348480\) \(3.2972\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331g1 has rank \(1\).

Complex multiplication

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

Modular form 422331.2.a.g

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