Properties

Label 21294bf
Number of curves $1$
Conductor $21294$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 21294bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.m1 21294bf1 \([1, -1, 0, -165060, 26192362]\) \(-141339344329/2167074\) \(-7625378117125314\) \([]\) \(161280\) \(1.8500\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21294bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21294bf do not have complex multiplication.

Modular form 21294.2.a.bf

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