Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 21175.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.a1 21175y1 \([0, 0, 1, -996875, -383097344]\) \(210720960000000/16807\) \(8738326953125\) \([]\) \(172800\) \(1.9288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175.a1 has rank \(0\).

Complex multiplication

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

Modular form 21175.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - q^{7} - 3 q^{9} - q^{13} + 2 q^{14} - 4 q^{16} + 3 q^{17} + 6 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display