Properties

Label 422370i
Number of curves $1$
Conductor $422370$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 422370i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422370.i1 422370i1 \([1, -1, 0, -5626187775, -162430147057559]\) \(-83725248159695345419/212089987460\) \(-49891906906298952911626860\) \([]\) \(372643200\) \(4.1689\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422370i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 422370i do not have complex multiplication.

Modular form 422370.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 3 q^{7} - q^{8} + q^{10} - 2 q^{11} + q^{13} + 3 q^{14} + q^{16} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display