Properties

Label 1638.i
Number of curves $1$
Conductor $1638$
CM no
Rank $0$

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

Elliptic curves in class 1638.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.i1 1638b1 \([1, -1, 0, -33738, -2381068]\) \(-215773279370739/447469568\) \(-8807543506944\) \([]\) \(5280\) \(1.3697\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1638.i1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1638.i do not have complex multiplication.

Modular form 1638.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} + q^{7} - q^{8} - 3 q^{10} + q^{11} - q^{13} - q^{14} + q^{16} + 5 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display