Properties

Label 279174p
Number of curves $1$
Conductor $279174$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 279174p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.p1 279174p1 \([1, 1, 0, -14889, 969237]\) \(-15124197817/8276688\) \(-199779127691472\) \([]\) \(1216512\) \(1.4477\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 279174p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 279174p do not have complex multiplication.

Modular form 279174.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 5 q^{13} - q^{14} - 2 q^{15} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display