Properties

Label 21175j
Number of curves $1$
Conductor $21175$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 21175j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.e1 21175j1 \([1, -1, 1, -7305, 110322]\) \(36479025/16807\) \(19859833984375\) \([]\) \(90000\) \(1.2464\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175j1 has rank \(0\).

Complex multiplication

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

Modular form 21175.2.a.j

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