Properties

Label 1850.b
Number of curves $1$
Conductor $1850$
CM no
Rank $1$

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

Elliptic curves in class 1850.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.b1 1850b1 \([1, 0, 1, -1, -12]\) \(-625/2368\) \(-59200\) \([]\) \(216\) \(-0.40534\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1850.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1850.b do not have complex multiplication.

Modular form 1850.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - q^{8} + q^{9} + 4 q^{11} - 2 q^{12} + 2 q^{13} + q^{16} - 8 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display