Properties

Label 21175t
Number of curves $1$
Conductor $21175$
CM no
Rank $1$

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

Elliptic curves in class 21175t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.y1 21175t1 \([1, -1, 0, -883867, -144187334]\) \(36479025/16807\) \(35182907353193359375\) \([]\) \(990000\) \(2.4453\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21175t do not have complex multiplication.

Modular form 21175.2.a.t

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