Properties

Label 21675w
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 21675w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.u1 21675w1 \([1, 0, 1, -6307576, 1138523423]\) \(35242105/19683\) \(15500315602553776171875\) \([]\) \(1156680\) \(2.9482\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 21675.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} - 3 q^{8} + q^{9} + 4 q^{11} - q^{12} - q^{13} + 2 q^{14} - q^{16} + q^{18} + O(q^{20})\) Copy content Toggle raw display