Properties

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

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

Elliptic curves in class 1638.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.g1 1638a1 \([1, -1, 0, 741, 21797]\) \(2284322013/11927552\) \(-234770006016\) \([]\) \(1632\) \(0.86397\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1638.g1 has rank \(0\).

Complex multiplication

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

Modular form 1638.2.a.g

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