Properties

Label 847.b
Number of curves $1$
Conductor $847$
CM no
Rank $1$

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

Elliptic curves in class 847.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
847.b1 847b1 \([0, 0, 1, 242, -333]\) \(884736/539\) \(-954871379\) \([]\) \(480\) \(0.41229\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 847.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 847.b do not have complex multiplication.

Modular form 847.2.a.b

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