Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 21675u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.z1 21675u1 \([0, 1, 1, -4626408, -549552031]\) \(100471803904/56953125\) \(6207674773546142578125\) \([]\) \(2467584\) \(2.8716\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21675u1 has rank \(1\).

Complex multiplication

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

Modular form 21675.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + q^{9} - q^{11} + 2 q^{12} + 4 q^{13} - 8 q^{14} - 4 q^{16} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display