Properties

Label 281775.g
Number of curves $1$
Conductor $281775$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 281775.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.g1 281775g1 \([0, 1, 1, -364508, 82308644]\) \(1186118904991744/36374479245\) \(164253507840703125\) \([]\) \(5087232\) \(2.0791\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 281775.g1 has rank \(2\).

Complex multiplication

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

Modular form 281775.2.a.g

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