Properties

Label 21175bk
Number of curves $1$
Conductor $21175$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 21175bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.k1 21175bk1 \([1, 0, 0, -190638, -32032483]\) \(9150625/7\) \(586137565234375\) \([]\) \(102960\) \(1.7659\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175bk1 has rank \(0\).

Complex multiplication

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

Modular form 21175.2.a.bk

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} - 2 q^{9} - q^{12} - 2 q^{13} - q^{14} - q^{16} - 4 q^{17} + 2 q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display