Properties

Label 279174.a
Number of curves $1$
Conductor $279174$
CM no
Rank $2$

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

Elliptic curves in class 279174.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
279174.a1 279174a1 \([1, 1, 0, -507, 9825]\) \(-2942649737/7154196\) \(-35148564948\) \([]\) \(408576\) \(0.71164\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 279174.a1 has rank \(2\).

Complex multiplication

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

Modular form 279174.2.a.a

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