Properties

Label 397488ex
Number of curves $1$
Conductor $397488$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 397488ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397488.ex1 397488ex1 \([0, -1, 0, -568416, 115728768]\) \(249395415529/73513818\) \(5986925741613293568\) \([]\) \(11612160\) \(2.3088\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 397488ex1 has rank \(1\).

Complex multiplication

The elliptic curves in class 397488ex do not have complex multiplication.

Modular form 397488.2.a.ex

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