Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 21175.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.l1 21175bf1 \([1, 0, 0, -888, 10517]\) \(-148955/7\) \(-3639453125\) \([]\) \(11520\) \(0.59758\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21175.l1 has rank \(1\).

Complex multiplication

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

Modular form 21175.2.a.l

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