Properties

Label 208725j
Number of curves $1$
Conductor $208725$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 208725j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.a1 208725j1 \([0, -1, 1, -303508, -73046832]\) \(-111701610496/18862875\) \(-522136464029296875\) \([]\) \(6451200\) \(2.1265\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 208725j do not have complex multiplication.

Modular form 208725.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{6} - 5 q^{7} + q^{9} - 2 q^{12} - 6 q^{13} + 10 q^{14} - 4 q^{16} + q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display