Properties

Label 216384.o
Number of curves $1$
Conductor $216384$
CM no
Rank $1$

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

Elliptic curves in class 216384.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.o1 216384cp1 \([0, -1, 0, -5217, 170241]\) \(-174676879/35328\) \(-3176530968576\) \([]\) \(552960\) \(1.1214\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216384.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 216384.o do not have complex multiplication.

Modular form 216384.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} + 2 q^{11} + 7 q^{13} + 3 q^{15} + 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display