Properties

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

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 21294y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.y1 21294y1 \([1, -1, 0, 846, -428]\) \(41781923/24192\) \(-38746221696\) \([]\) \(16128\) \(0.72116\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21294y1 has rank \(1\).

Complex multiplication

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

Modular form 21294.2.a.y

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