Properties

Label 100016.e
Number of curves $1$
Conductor $100016$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 100016.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100016.e1 100016h1 \([0, -1, 0, 209, -5158]\) \(62800480256/735423899\) \(-11766782384\) \([]\) \(43008\) \(0.61330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100016.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100016.e do not have complex multiplication.

Modular form 100016.2.a.e

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