Properties

Label 66248.e
Number of curves $1$
Conductor $66248$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 66248.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66248.e1 66248x1 \([0, 1, 0, 8866191, -6672120701]\) \(530208386048/439239619\) \(-63854252520525775969024\) \([]\) \(5419008\) \(3.0636\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66248.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66248.e do not have complex multiplication.

Modular form 66248.2.a.e

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