Properties

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

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 422331bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.bi1 422331bi1 \([0, 1, 1, -11041, 484033]\) \(-629407744/70227\) \(-16609643466507\) \([]\) \(1404000\) \(1.2740\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331bi1 has rank \(1\).

Complex multiplication

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

Modular form 422331.2.a.bi

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