Properties

Label 281775q
Number of curves $1$
Conductor $281775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 281775q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.q1 281775q1 \([1, 0, 0, -328888, -75538483]\) \(-417267265/19773\) \(-186434434311328125\) \([]\) \(3444480\) \(2.0766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 281775q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 281775q do not have complex multiplication.

Modular form 281775.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} - 3 q^{7} + 3 q^{8} + q^{9} + q^{11} - q^{12} - q^{13} + 3 q^{14} - q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display