Properties

Label 10164x
Number of curves $1$
Conductor $10164$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 10164x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10164.q1 10164x1 \([0, 1, 0, -2702, -65331]\) \(-76995328/18711\) \(-530362845936\) \([]\) \(14400\) \(0.96820\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 10164x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 10164x do not have complex multiplication.

Modular form 10164.2.a.x

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