Properties

Label 281775.a
Number of curves $1$
Conductor $281775$
CM no
Rank $1$

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

Elliptic curves in class 281775.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.a1 281775a1 \([0, -1, 1, -98956008, -378860127832]\) \(-57834888040448/823875\) \(-1526587292952591796875\) \([]\) \(60632064\) \(3.2044\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 281775.a1 has rank \(1\).

Complex multiplication

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

Modular form 281775.2.a.a

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