Properties

Label 208725.i
Number of curves $1$
Conductor $208725$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 208725.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.i1 208725b1 \([0, 1, 1, -458, 31994]\) \(-45056/1863\) \(-440279296875\) \([]\) \(395520\) \(0.91434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725.i1 has rank \(1\).

Complex multiplication

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

Modular form 208725.2.a.i

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