Properties

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

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 21175.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.bd1 21175g1 \([1, 1, 0, -7625, -259310]\) \(9150625/7\) \(37512804175\) \([]\) \(20592\) \(0.96115\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175.bd1 has rank \(0\).

Complex multiplication

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

Modular form 21175.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - q^{7} - 3 q^{8} - 2 q^{9} + q^{12} + 2 q^{13} - q^{14} - q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display