Properties

Label 500921.b
Number of curves $1$
Conductor $500921$
CM no
Rank $1$

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

Elliptic curves in class 500921.b

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
500921.b1 \([1, -1, 0, -68, -197]\) \(35062107417/500921\) \(500921\) \([]\) \(55576\) \(-0.10195\)

Rank

sage: E.rank()
 

The elliptic curve 500921.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 500921.b do not have complex multiplication.

Modular form 500921.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 3 q^{5} + 3 q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - q^{11} + 3 q^{14} - q^{16} + 3 q^{17} - 3 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display