Properties

Label 31939a
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 31939a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31939.d1 31939a1 \([0, 1, 1, -45947, -5379029]\) \(-32768/19\) \(-6220256753485259\) \([]\) \(114800\) \(1.7333\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 31939.2.a.a

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