Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1638.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1638.o1 1638o1 \([1, -1, 1, -68, 263]\) \(-47045881/8736\) \(-6368544\) \([]\) \(320\) \(0.030051\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1638.o1 has rank \(1\).

Complex multiplication

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

Modular form 1638.2.a.o

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