Properties

Label 84966.r
Number of curves $1$
Conductor $84966$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 84966.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.r1 84966g1 \([1, 1, 0, -3575947, -3610622147]\) \(-301935091801/161243136\) \(-2700628006834982117376\) \([]\) \(4725864\) \(2.8163\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 84966.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 84966.r do not have complex multiplication.

Modular form 84966.2.a.r

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