Properties

Label 21675t
Number of curves $1$
Conductor $21675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 21675t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.i1 21675t1 \([1, 0, 0, -873, 1782]\) \(35242105/19683\) \(41098596075\) \([]\) \(13608\) \(0.72688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21675t1 has rank \(1\).

Complex multiplication

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

Modular form 21675.2.a.t

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