Properties

Label 258570.fn
Number of curves $1$
Conductor $258570$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("fn1")
 
E.isogeny_class()
 

Elliptic curves in class 258570.fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
258570.fn1 258570fn1 \([1, -1, 1, -162845897, 217464682569]\) \(4752182606640001/2546899200000\) \(255960416617896548563200000\) \([]\) \(118609920\) \(3.7585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 258570.fn1 has rank \(0\).

Complex multiplication

The elliptic curves in class 258570.fn do not have complex multiplication.

Modular form 258570.2.a.fn

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 3 q^{7} + q^{8} + q^{10} - 5 q^{11} + 3 q^{14} + q^{16} - q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display