Properties

Label 1849.a
Number of curves $1$
Conductor $1849$
CM no
Rank $0$

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

Elliptic curves in class 1849.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1849.a1 1849c1 \([1, 1, 1, -71225, 1841958]\) \(1849\) \(21611482313284249\) \([]\) \(9030\) \(1.8253\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1849.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1849.a do not have complex multiplication.

Modular form 1849.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{7} + 3 q^{8} - 2 q^{9} - q^{10} + q^{12} - 5 q^{13} + 3 q^{14} - q^{15} - q^{16} + 3 q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display