Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1638.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.a1 1638f1 \([1, -1, 0, -904356, 333142096]\) \(-112205650221491190337/745029571313664\) \(-543126557487661056\) \([]\) \(38080\) \(2.2386\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1638.a1 has rank \(0\).

Complex multiplication

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

Modular form 1638.2.a.a

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