Properties

Label 1849b
Number of curves $1$
Conductor $1849$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1849b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1849.c1 1849b1 \([1, 0, 1, -39, -27]\) \(1849\) \(3418801\) \([]\) \(210\) \(-0.055260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1849b1 has rank \(1\).

Complex multiplication

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

Modular form 1849.2.a.b

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