Properties

Label 21675.w
Number of curves $1$
Conductor $21675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 21675.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.w1 21675n1 \([0, -1, 1, -204708, -31348807]\) \(69632/9\) \(122620736267578125\) \([]\) \(342720\) \(2.0076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21675.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21675.w do not have complex multiplication.

Modular form 21675.2.a.w

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} + q^{9} + 3 q^{11} - 2 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} + 2 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display