Properties

Label 31939.b
Number of curves $1$
Conductor $31939$
CM no
Rank $1$

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

Elliptic curves in class 31939.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31939.b1 31939e1 \([1, 1, 1, 10051, 452254]\) \(14063/19\) \(-151713579353299\) \([]\) \(137760\) \(1.4068\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31939.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 31939.b do not have complex multiplication.

Modular form 31939.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2q^{3} - q^{4} + 3q^{5} - 2q^{6} + 4q^{7} + 3q^{8} + q^{9} - 3q^{10} - 4q^{11} - 2q^{12} - 2q^{13} - 4q^{14} + 6q^{15} - q^{16} - 3q^{17} - q^{18} + q^{19} + O(q^{20})\)  Toggle raw display