Properties

Label 21175.q
Number of curves $1$
Conductor $21175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 21175.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.q1 21175bd1 \([1, -1, 1, -35355, -1146428]\) \(36479025/16807\) \(2251706070604375\) \([]\) \(198000\) \(1.6406\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21175.q do not have complex multiplication.

Modular form 21175.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} - q^{4} - 3 q^{6} - q^{7} + 3 q^{8} + 6 q^{9} - 3 q^{12} - 6 q^{13} + q^{14} - q^{16} - 6 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display