Properties

Label 49686.w
Number of curves $1$
Conductor $49686$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 49686.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49686.w1 49686n1 \([1, 1, 0, 49514, -4124882]\) \(68921/78\) \(-15192773969104914\) \([]\) \(376320\) \(1.7914\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49686.w1 has rank \(0\).

Complex multiplication

The elliptic curves in class 49686.w do not have complex multiplication.

Modular form 49686.2.a.w

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