Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31939.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31939.a1 31939c1 \([1, 0, 0, 6, 7]\) \(14063/19\) \(-31939\) \([]\) \(3360\) \(-0.44994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31939.a1 has rank \(1\).

Complex multiplication

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

Modular form 31939.2.a.a

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