Properties

Label 8619.m
Number of curves $1$
Conductor $8619$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8619.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8619.m1 8619f1 \([0, -1, 1, -56, -271]\) \(-692224/867\) \(-24762387\) \([]\) \(5232\) \(0.11211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8619.m1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8619.m do not have complex multiplication.

Modular form 8619.2.a.m

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